Excel 2013 for human resource management statistics a guide to solving practical problems

Mean

The mean, often referred to as the "arithmetic average," represents the central value of a set of scores When my daughter, a fifth grader, came home upset about not understanding averages, I took the opportunity to explain how to calculate the mean using her textbook.

"Jennifer, to calculate the average, simply add all the scores together and divide by the total count of numbers." She shot me a serious glance and replied, "Dad, this is serious!" believing I was joking.

“See these numbers in your book; add them up What is the answer?” (She did that.)

“Now, how many numbers do you have?” (She answered that question.)

“Then, take the number you got when you added up the numbers, and divide that number by the number of numbers that you have.”

By applying the same reasoning, you can easily find the correct answer, as Excel will automate all the necessary steps for you.

We will call this average of the scores the “mean” which we will symbolize as:

X, and we will pronounce it as: “Xbar.”

The formula for finding the mean with your calculator looks like this:

XẳΣX n ð1:1ị © Springer International Publishing Switzerland 2016

T.J Quirk, J Palmer-Schuyler, Excel 2013 for Human Resource

Management Statistics, Excel for Statistics, DOI 10.1007/978-3-319-28982-3_1

The Greek letter sigma (Σ) represents the concept of "sum." It instructs you to add all the values denoted by the letter X and then divide the total by n, which signifies the count of the numbers involved.

Subordinate ratings of supervisor performance are crucial in human resources management For instance, if you aim to enhance your Excel skills, you can analyze survey data where subordinates rate their supervisors on key behaviors using a scale from 1 (Low) to 7 (High) Consider a random sample of six ratings focused on the quality of supervision provided by supervisors to their subordinates.

To find the mean of these scores, you add them up, and then divide by the number of scores So, the mean is: 25/6ẳ4.17.

To learn more about the mean of a set of scores, see Aamodt et al (2007) andWhetzel and Wheaton (2007).

Standard Deviation

Standard deviation measures the proximity of scores to the mean, indicating how closely they are grouped A small standard deviation signifies that the scores are tightly clustered around the mean, while a large standard deviation indicates a wider dispersion of scores The formula for standard deviation, represented by the symbol S, provides a quantitative assessment of this spread.

The formula look complicated, but what it asks you to do is this:

1 Subtract the mean from each scoreðXXị.

2 Then, square the resulting numbers to make each a positive number.

3 Then, add up these squared numbers to get a total score.

4 Then, take this total score and divide it by n1 (where n stands for the number of numbers that you have).

5 The final step is to take the square root of the number you found in step 4.

2 1 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean

This article does not require you to calculate standard deviation manually, as you can refer to basic statistics books for examples Instead, we will demonstrate how to use Excel to compute the standard deviation of a set of scores For instance, when applying Excel to the six numbers mentioned earlier, the standard deviation (STDEV) is found to be 1.47.

Standard Error of the Mean

The formula for the standard error of the mean (s.e., which we will use S X to symbolize) is: s:e:ẳSX ẳ S

To calculate the standard error (s.e.), divide the standard deviation (STDEV) by the square root of n, where n represents the total number of values in your data set For instance, in the previous example, the standard error is 0.60, which can be verified using a calculator.

If you want to learn more about the standard deviation and the standard error of the mean, see Black (2010) and Levine (2011).

In this article, we will explore how to utilize Excel to calculate key statistical measures, including sample size, mean, standard deviation, and standard error of the mean, using the monthly salaries of employees classified as "Semi-professional" in your organization The hypothetical data for this analysis is presented in Fig.1.1.

Fig 1.1 Worksheet Data for Monthly Salary

1.3 Standard Error of the Mean 3

Sample Size, Mean, Standard Deviation, and Standard

Using the Fill/Series/Columns Commands

Objective: To add the numbers 2–8 in the Employee column underneath

Home (top left of screen)

Fill (top right of screen: click on the Series down arrow; see Fig.1.2)

Fig 1.2 Home/Fill/Series commands

To identify employee numbers, label them from 1 to 8, placing the number 8 in cell B11 Next, input the monthly salary figures into cells C4 through C11, ensuring that you verify your entries for accuracy to obtain the correct results.

Since your computer screen shows the information in a format that does not look professional, you need to learn how to “widen the column width” and how to

“center the information” in a group of cells Here is how you can do those two steps:

Changing the Width of a Column

Objective: To make a column width wider so that all of the information fits inside that column

To ensure all information is visible in Column C, adjust its width by expanding the column size on your computer screen.

Click on the letter, C, at the top of your computer screen

Place your mouse pointer on your computer at the far right corner of C until you create a “cross sign” on that corner

Left-click on your mouse, hold it down, and move this corner to the right until it is

“wide enough to fit all of the data”

To adjust the new column width, simply lift your finger off the mouse (refer to Fig 1.4) Additionally, Fig 1.3 illustrates the dialogue box for the Fill/Series/Columns/Step Value/Stop Value commands, which are essential for managing sample size, mean, standard deviation, and standard error of the mean.

Then, click on any empty cell (i.e., any blank cell) to “deselect” column C so that it is no longer a darker color on your screen.

When you widen a column, you will make all of the cells in all of the rows of this column that same width.

Now, let’s go through the steps to center the information in both Column B andColumn C.

Centering Information in a Range of Cells

Objective: To center the information in a group of cells

In order to make the information in the cells look “more professional,” you can center the information using the following steps:

Left-click your mouse pointer on B3 and drag it to the right and down to highlight cells B3:C11 so that these cells appear in a darker color

At the top of your computer screen, you will find a series of lines that are uniformly centered in width under the "Alignment" settings, which can be accessed by clicking the second icon in the bottom left corner of the Alignment box (refer to Fig 1.5).

Fig 1.4 Example of How to Widen the Column Width

Click on this icon to center the information in the selected cells (see Fig.1.6).

To simplify referencing the monthly salaries of semi-professional employees in your formulas, it's beneficial to name the data range instead of recalling specific cell locations (C4:C11) For instance, you can designate this group of cells as "salary," though you have the flexibility to choose any name that suits your preference.

Fig 1.5 Example of How to Center Information

Centering Information in the Cells

1.4 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean 7

Naming a Range of Cells

Objective: To name the range of data for monthly salary with the name: salary

Highlight cells C4:C11 by left-clicking your mouse pointer on C4 and dragging it down to C11

Formulas (top left of your screen)

Define Name (top center of your screen) salary (type this name in the top box; see Fig.1.7)

Then, click on any cell of your spreadsheet that does not have any information in it (i.e., it is an “empty cell”) to deselect cells C4:C11

Now, add the following terms to your spreadsheet:

Fig 1.7 Dialogue box for “naming a range of cells” with the name: salary

When using formulas in Excel, it is essential to start each formula with an equal sign (ẳ) to indicate to the program that you are entering a formula This practice ensures that Excel recognizes your input as a calculation rather than plain text, allowing for accurate data processing and analysis.

Finding the Sample Size Using

Objective: To find the sample size (n) for these data using the ẳCOUNT function

This command should insert the number 8 into cell F6 since there are eight employees in your sample.

Finding the Mean Score Using the ẳ AVERAGE

Objective: To find the mean salary figure using theẳAVERAGE function

This command should insert the number 2516.25 into cell F9.

Fig 1.8 Example of Entering the Sample Size, Mean, STDEV, and s.e Labels

1.4 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean 9

Finding the Standard Deviation Using the ẳ STDEV

Objective: To find the standard deviation (STDEV) using the ẳSTDEV function

This command should insert the number 350.2321 into cell F12.

Finding the Standard Error of the Mean

Objective: To find the standard error of the mean using a formula for these eight data points

This command should insert the number 123.8257 into cell F15 (see Fig.1.9).

It is crucial to verify that all figures in your spreadsheet are accurately placed in their respective cells, as any discrepancies will lead to incorrect formula calculations.

Fig 1.9 Example of Using Excel Formulas for Sample Size, Mean, STDEV, and s.e.

1.4.8.1 Formatting Numbers in Number Format (Two Decimal Places)

Objective: To convert the mean, STDEV, and s.e to one decimal place

Home (top left of screen)

To decrease the number of decimal places displayed in your document, locate the "Number" section at the top center of your screen Then, move your mouse pointer to the bottom right corner of the decimal display (noted as 00.0) until the option "Decrease Decimal" appears.

Click on this icononce and notice that the cells F9:F15 are now all in just one decimal place (see Fig.1.11).

Fig 1.10 Using the “Decrease Decimal Icon” to convert Numbers to Fewer Decimal Places1.4 Sample Size, Mean, Standard Deviation, and Standard Error of the Mean 11

Now, click on any “empty cell” on your spreadsheet to deselect cells F9:F15.

But, since salary figures are typically in two decimal places, let’s change the Mean, STDEV, and s.e figures to two decimal places by:

Number (top center of screen)

Click on the down arrow to the right of Number at top center of screen

Click on: Number (in the list of possible formats on the left)

Change to two decimal places (in the right center of the screen)

Cells F9:F15 should now be in two decimal places.

Saving a Spreadsheet

Objective: To save this spreadsheet with the name: SALARY3

To ensure you can access your spreadsheet later, the first step is to choose the appropriate location for saving it You have multiple options, including saving it directly to your computer's hard drive If you're unsure how to do this, consider asking someone for assistance.

Converting Numbers to One Decimal Place

Or, you can save it onto a “CD” or onto a “flash drive.” To save a spreadsheet, you need to complete these steps:

To save your file, simply scroll through the left sidebar to select your desired location, such as My Documents, and click on it to complete the saving process.

File name: SALARY3 (enter this name to the right of File name; see Fig.1.12)

Important note: Be very careful to save your Excel file spreadsheet every few minutes so that you do not lose your information!

Fig 1.12 Dialogue Box of Saving an Excel Workbook File as “SALARY3” in My Documents location

Printing a Spreadsheet

Objective: To print the spreadsheet

Use the following procedure when printing any spreadsheet.

Print Active Sheets (see Fig.1.13)

Print (top of your screen)

The final spreadsheet is given in Fig.1.14.

Fig 1.13 Example of How to Print an Excel Worksheet

Using the File/Print/Print

Before concluding this chapter, let's practice formatting figures in a spreadsheet through two examples: first, applying two decimal places for dollar amounts, and second, utilizing three decimal places for numerical figures.

Close your spreadsheet by: File/Close/Don’t Save, and open a blank Excel spreadsheet by using File/New/Blank Workbook (on the top left of your screen).

Formatting Numbers in Currency Format (Two Decimal Places)

Objective: To change the format of figures to dollar format with two decimal places

Highlight cells A4:A6 by left-clicking your mouse on A4 and dragging it down so that these three cells are highlighted in a darker color

Number (top center of screen: click on the down arrow on the right; see Fig.1.15). Fig 1.14 Final Result of Printing an Excel Spreadsheet

1.7 Formatting Numbers in Currency Format (Two Decimal Places) 15

Decimal places: 2 (then see Fig.1.16)

The three cells should have a dollar sign in them and be in two decimal places. Next, let’s practice formatting figures in number format, three decimal places.

Fig 1.15 Dialogue Box for Number Format Choices

Fig 1.16 Dialogue Box for Currency (two decimal places) Format for Numbers

Formatting Numbers in Number Format (Three Decimal Places)

Objective: To format figures in number format, three decimal places

Highlight cells A4:A6 on your computer screen

Number (click on the down arrow on the right)

At the right of the box, change two decimal places to three decimal places by clicking on the “up arrow” once

To format the three figures in number format with three decimal places, first click on any blank cell to deselect cells A4:A6 Then, close the file by navigating to File > Close > Don’t Save, as saving is unnecessary for this practice problem Additionally, you can apply similar commands to format a range of cells in percentage format or other formats, specifying the desired number of decimal places.

End-of-Chapter Practice Problems

Employee morale surveys are crucial for HR departments, enabling top management to understand employee attitudes and address potential issues proactively Analyzing data from a recent HR survey focused on middle managers will provide insights into their perspectives, particularly regarding Item #21 This analysis will help enhance management strategies and improve overall workplace morale.

1.9 End-of-Chapter Practice Problems 17

To analyze the data effectively, utilize Excel to calculate the sample size, mean, standard deviation, and standard error of the mean Ensure to label each result clearly and round the mean, standard deviation, and standard error to two decimal places, applying the appropriate number format for these values.

(b) Print the result on a separate page.

(c) (c) Save the file as: MGT21

On-time performance is a crucial metric for evaluating employee punctuality in any organization To assess the average percentage of on-time arrivals for workers in Department D over the past month, refer to the data presented in Fig 1.18.

Fig 1.17 Worksheet Data for Chap 1: Practice Problem #1

To analyze the data effectively, create a table in Excel and calculate the sample size, mean, standard deviation, and standard error of the mean Ensure to label each result clearly and round the mean, standard deviation, and standard error of the mean to one decimal place using the appropriate number format.

(c) Save the file as: ONTIME3

Employee absence poses a significant challenge for organizations, often escalating if not effectively monitored by the Human Resources department While legitimate reasons for absence include illness, family emergencies, personal business, vacations, and holidays, factors such as low job satisfaction, inadequate pay, poor supervision, and excessive workload stress can also contribute to increased absenteeism High levels of absence may indicate potential employee turnover To manage this issue, companies must maintain accurate time records and establish a standard for acceptable absence rates.

Monthly absence rateẳWDL=ðHCWDị where WDLẳtotal number of worker days lost through absence that month

HCẳaverage number of employees that month

WDẳtotal number of workdays in that month

Suppose that you wanted to determine the descriptive statistics summarizing your company’s monthly absence rate during the past year The hypothetical data are given in Fig.1.19:

Fig 1.18 Worksheet Data for Chap 1: Practice

To analyze the data effectively, utilize Excel to construct a table Next, calculate the sample size, mean, standard deviation, and standard error of the mean, placing these results to the right of the table Ensure to label each of your findings clearly, rounding the mean, standard deviation, and standard error of the mean to one decimal place using the number format.

(c) Save the file as: ABSENCE3

Aamodt M, Surrette M, and Cohen D Understanding statistics: a guide for I/O psychologists and human resource professionals Belmont: Wadsworth Cengage Learning; 2007.

Black K Business statistics: for contemporary decision making 6 th ed Hoboken: John Wiley

Davis J H Statistics for compensation: a practical guide to compensation analysis Hoboken: John Wiley & Sons; 2011.

Levine D M Statistics for managers using Microsoft Excel 6 th ed Boston: Prentice Hall/Pearson; 2011.

Weiers R M Introduction to business statistics 7 th ed Mason: South-Western Cengage Learning; 2011.

Whetzel D L and Wheaton G R (Eds.) Applied measurement: industrial psychology in human resources management Mahwah: Lawrence Erlbaum Associates; 2007.

Fig 1.19 Worksheet Data for Chap 1: Practice

To assist a Human Resources administrator in forming an in-house focus group, it is essential to create a random sample of 5 out of 32 mid-level managers This sampling process requires defining a "sampling frame," which serves as the basis for selecting participants By utilizing Excel skills, you can effectively generate this random sample, enabling the administrator to reach out and coordinate a meeting time for discussing innovative employee benefit ideas.

A sampling frame is essential for selecting a random sample, and in this case, it consists of a group of 32 managers To establish the sampling frame, each manager must be assigned a unique identifier, beginning with ID 1 for the first manager, ID 2 for the second, and continuing sequentially until the last manager, who receives ID 32.

Since the group had 32 managers, your sampling frame would go from 1 to

32 with each manager having a unique ID number.

We will first create the frame numbers as follows in a new Excel worksheet:

Creating Frame Numbers for Generating

Objective: To create the frame numbers for generating random numbers

To create frame numbers in column A using the Home/Fill commands, follow these steps: Start by entering the number 1 in cell A1 Next, select the cell and drag the fill handle down to cell A35, ensuring that the sequence continues up to 32 This will automatically populate the cells with consecutive numbers, culminating with the number 32 in cell A35.

Click on cell A4 to select this cell

Fill (then click on the “down arrow” next to this command and select)

Then, save this file as: Random29 You should obtain the result in Fig.2.3.

Fig 2.1 Dialogue Box for Fill/Series Commands

Fig 2.2 Dialogue Box for Fill/Series/Columns/Step value/Stop value Commands

Now, create a column next to these frame numbers in this manner:

To organize your spreadsheet, utilize the Home/Fill command to populate frame numbers from cell B4 to B35 Ensure that columns A and B are widened to accommodate all content, and center the data within both columns for a neat appearance, as illustrated in Fig 2.4.

Fig 2.3 Frame Numbers from 1 to 32

2.1 Creating Frame Numbers for Generating Random Numbers 23

Save this file as: Random30

You may be questioning the duplication of information in both Column A and Column B of your spreadsheet This approach ensures that you have precisely 32 frame numbers before you begin sorting them into a random sequence.

Now, let’s add a random number to each of the duplicate frame numbers as follows:

Creating Random Numbers in an Excel Worksheet

(then widen columns A, B, C so that their labels fit inside the columns; then center the information in A3:C35)

Next, hit the Enter key to add a random number to cell C4.

To generate a random number in Excel, you must use the RAND() function, which requires both an open and a closed parenthesis The RAND() command retrieves a random value by referencing the cell to its left, assigning the generated number to the cell containing the function.

To add a random number to all 32 ID frame numbers, position your mouse pointer over cell C4 and drag it to the bottom right corner until a “plus sign” appears Then, click and drag down to cell C35.

Then, click on any empty cell to deselect C4:C35 to remove the dark color highlighting these cells.

Now, let’s sort these duplicate frame numbers into a random sequence:

Random Numbers Assigned to the Duplicate Frame

2.2 Creating Random Numbers in an Excel Worksheet 25

Sorting Frame Numbers into a Random Sequence

Objective: To sort the duplicate frame numbers into a random sequence

Highlight cells B3:C35 (include the labels at the top of columns B and C) Data (top of screen)

Sort (click on this word at the top center of your screen; see Fig.2.6)

Sort by: RANDOM NO (click on the down arrow)

Smallest to Largest (see Fig.2.7)

Fig 2.6 Dialogue Box for Data/Sort Commands

Click on any empty cell to deselect B3:C35.

These steps will produce Fig.2.8with the DUPLICATE FRAME NUMBERS sorted into a random order:

Important note: Because Excel randomly assigns these random numbers, your

Excel commands will produce a different sequence of random numbers from everyone else who reads this book!

Fig 2.7 Dialogue Box for Data/Sort/RANDOM NO./Smallest to Largest Commands

2.3 Sorting Frame Numbers into a Random Sequence 27

Because your objective at the beginning of this chapter was to select randomly

To conduct a focus group session, select the first five mid-level managers from the sorted ID numbers in the DUPLICATE FRAME NO column, out of the 32 available in your organization.

In this chapter, we will choose five unique manager IDs, which will differ from the random numbers previously selected, utilizing the method illustrated in Fig 2.9.

When using the RAND() function in Excel, the five ID numbers generated from your random sort will differ from those shown in Fig 2.9, as Excel produces a new random number each time the command is executed.

Before concluding this chapter, it's essential to understand how to print a file so that all its information fits neatly on a single page, avoiding any overflow onto additional pages.

Printing an Excel File So That All of the Information

Objective: To print a file so that all of the information fits onto one page

2.4 Printing an Excel File So That All of the Information Fits onto One Page 29

This chapter concludes with three practice problems that involve sorting random numbers from files containing 63 students, 114 employees, and 75 new hires To ensure these files fit onto a single printed page, proper formatting is essential, as they may otherwise be too large to print in their original state.

Let’s create a situation where the file does not fit onto one printed page unless you format it first to do that.

Go back to the file you just created, Random 33, and enter the name:Jennifer into cell: A50.

Printing this file will result in the name "Jennifer" appearing on a second page, as it extends beyond the designated page range in its current format.

To ensure that all information, including the name Jennifer, fits onto a single page when printing, you need to adjust the page format by following specific steps.

Click on any empty cell to change your location away from cell A50

Page Layout (top left of the computer screen)

(Notice the “Scale to Fit” section in the center of your screen; see Fig.2.10)

Hit the down arrow to the right of 100 %once to reduce the size of the page to 95 %

In Figure 2.11, Jennifer's name appears on a second page, positioned below the horizontal dotted line that indicates the outline dimensions of the file as it would appear if printed.

Fig 2.10 Dialogue Box for Page Layout/Scale to Fit Commands

To adjust the worksheet size to 90% of its original dimensions, simply press the down arrow on the right once more to repeat the “scale change steps.” As shown in Fig 2.12, the dotted lines on your screen now appear below Jennifer's name, signifying that all content, including her name, is formatted to fit on a single printed page.

Save the file as: Random34

Print the file Does it all fit onto one page? It should (see Fig.2.13).

Fig 2.11 Example of Scale Reduced to 95 % with “Jennifer” to be Printed on a Second Page

Fig 2.12 Example of Scale Reduced to 90 % with “Jennifer” to be printed on the first page (note the dotted line below Jennifer on your screen)

2.4 Printing an Excel File So That All of the Information Fits onto One Page 31

End-of-Chapter Practice Problems

As the Director of a Master's degree program in Human Resources, I plan to conduct interviews with a random sample of students graduating this June to gather their insights and suggestions for enhancing the program This initiative aims to identify areas for improvement and ensure that the curriculum meets the evolving needs of future HR professionals By engaging with students directly, we can foster a collaborative environment that values their feedback and contributes to the continuous development of our program.

Spreadsheet of 90 % Scale to Fit

Suppose that you have 63 Master’s students who are scheduled to graduate You want to randomly select 15 of these 63 students for a personal interview.

(a) Set up a spreadsheet of frame numbers for these students with the heading: FRAME NUMBERS using the Home/Fill commands.

To organize your data, first create a column labeled "Duplicate Frame Numbers" adjacent to the original frame numbers Next, add another column titled "RANDOM NO." to the right of the duplicate frame numbers In this new column, utilize the =RAND() function to generate random numbers corresponding to each frame number, ensuring to format the column to display three decimal places for each random value.

(d) Sort the duplicate frame numbers and random numbers into a random order. (e) Print the result so that the spreadsheet fits onto one page.

(f) Circle on your printout the I.D number of the first 15 students that you would use in your interviews.

(g) Save the file as: RAND9

It's important to understand that each time the =RAND() command is used in Excel, it generates a unique random order of student ID numbers Consequently, the sequence of random numbers presented in this Excel Guide will differ from the random sequence you create This variability is expected and normal when using the RAND function.

As the HR director of a large company, I plan to conduct phone interviews with 10 out of the 114 employees enrolled in our Vision Care Plan, which was implemented a year ago, to gather their feedback on the plan's effectiveness and overall satisfaction.

(a) Set up a spreadsheet of frame numbers for these claims with the heading: FRAME NO.

To organize your data effectively, first create a column labeled "Duplicate frame no." next to the original frame numbers Then, add another column titled "Random number" to the right of the duplicate frame numbers, utilizing the =RAND() function to generate random numbers for each entry Finally, adjust the formatting of this column to display three decimal places for each random number.

(d) Sort the duplicate frame numbers and random numbers into a random order (e) Print the result so that the spreadsheet fits onto one page

(f) Circle on your printout the I.D number of the first 10 employees that would be used in this research study.

(g) Save the file as: RANDOM6

3 Suppose, for the sake of argument, that you are the Director of HR for a large company and that you want to conduct a personal interview with 20 of the

Recently, 75 new hires participated in a comprehensive one-day orientation program focused on the various employee benefits offered by the company To evaluate and enhance the effectiveness of this orientation, a random sample of 20 out of the 75 new hires will be selected for feedback This approach aims to gather insights on how to improve the orientation experience for future employees.

(a) Set up a spreadsheet of frame numbers for these new-hires with the heading: FRAME NUMBERS.

To organize your data, first create a column labeled "Duplicate Frame Numbers" next to the original frame numbers Then, add another column titled "Random Number" to the right of the duplicate frame numbers, utilizing the =RAND() function to generate random numbers for each entry Finally, format this column to display each random number with three decimal places.

(d) Sort the duplicate frame numbers and random numbers into a random order. (e) Print the result so that the spreadsheet fits onto one page.

(f) Circle on your printout the I.D number of the first 20 new-hires that you would select for your personal interview study.

(g) Save the file as: RAND5

Confidence Interval About the Mean Using the TINV Function and Hypothesis Testing

This chapter focuses on two ideas: (1) finding the 95 % confidence interval about the mean, and (2) hypothesis testing.

Let’s talk about the population mean and then about the confidence interval.

Confidence Interval About the Mean

How to Estimate the Population Mean

Objective: To estimate the population mean,μ

The population mean represents the average of a specific demographic within a target group, such as adults aged 25–44 For instance, assessing the preference of this age group for a new Ben & Jerry’s ice cream flavor would be impractical if we attempted to survey every individual in the U.S within that demographic due to the extensive time and high costs involved in conducting such a comprehensive study.

To estimate the mean of an entire population efficiently, we utilize a sample of individuals rather than testing everyone, which conserves both time and resources This method, known as "inferential statistics," allows us to draw conclusions about the population mean based on the sample mean.

When analyzing a sample from a population, we consider the sample size (n), the sample mean (X̄), and the sample standard deviation (STDEV) These metrics enable us to assess the reliability of our estimated population mean through a statistical method known as the "confidence interval for the mean."

Estimating the Lower Limit and the Upper Limit

of the 95 % Confidence Interval About the Mean

While this book does not delve into the theoretical background of the test, readers can explore it further in reputable statistics textbooks such as McDaniel and Gates (2010) or Black (2010) The fundamental concepts of the test are essential for a comprehensive understanding.

We assume that the population mean is somewhere in an interval which has a

In this book, we establish a "lower limit" and an "upper limit" for the population mean, aiming for a 95% confidence level that the true mean falls within this interval.

“We are 95 % confident that the population mean of the TIME TO FILL an approved application for staffing during the past 12 months was between 33 days and 37 days.”

If we want to claim that the TIME TO FILL during the past 12 months was

In our research study, we established a 95% confidence interval for the population mean, which ranges from 33 days to 37 days This indicates that we can confidently assert that the true population mean lies within this range Since 35 days falls within this interval, it is a plausible estimate of the population mean.

But we are only 95 % confident that the population mean is inside this interval, and 5 % of the time we will be wrong in assuming that the population mean is

In HR research, we aim for a 95% confidence level in our assumptions, although this is an arbitrary choice, as we could opt for 80%, 90%, or even 99% confidence Throughout this book, we will consistently maintain a 95% confidence level in our results, eliminating any uncertainty about the desired confidence for the problems presented This standardization ensures clarity and consistency in our findings.

So how do we find the 95 % confidence interval about the mean for our data?

In words, we will find this interval this way:

To calculate the confidence interval, first determine the sample mean (X̄) For the upper limit, add 1.96 times the standard error of the mean (s.e.) to the sample mean For the lower limit, subtract 1.96 times the standard error of the mean from the sample mean.

36 3 Confidence Interval About the Mean Using the TINV Function and Hypothesis

The standard error of the mean (s.e.) is calculated by dividing the sample's standard deviation (STDEV) by the square root of the sample size (n).

In mathematical terms, the formula for the 95 % confidence interval about the mean is:

To calculate the confidence interval, first determine the upper limit by adding 1.96 times the standard error (s.e.) to the mean Conversely, to find the lower limit, subtract 1.96 times the s.e from the mean The expression 1.96 s.e represents the product of 1.96 and the standard error of the mean, which is essential for computing the confidence interval.

Note: We will explain shortly where the number 1.96 came from.

Let’s try a simple example to illustrate this formula.

Estimating the Confidence Interval for TIME

To determine the average TIME TO FILL for staffing requisitions last year, a random sample of 40 job acceptances was analyzed, revealing an average acceptance time of 36 days with a standard deviation of 4 days The standard error, calculated as 4 divided by the square root of 40, is approximately 0.63 days.

The 95 % confidence interval for these data would be:

Theupper limit of this confidence intervaluses the plus sign of thesign in the formula Therefore, the upper limit would be:

Similarly, the lower limit of this confidence interval uses the minus sign of thesign in the formula Therefore, the lower limit would be:

The result of our part of the ongoing research study would, therefore, be the following:

“We are 95 % confident that the population mean for TIME TO FILL during the past

12 months was between 34.77 days and 37.23 days.”

3.1 Confidence Interval About the Mean 37

Based on our analysis, we can conclude that the average time to fill positions over the past 12 months is 35 days, as this figure falls within the 95% confidence interval for the population mean Our data strongly supports this assertion, confirming the reliability of the 35-day average.

You are probably asking yourself: “Where did that 1.96 in the formula come from?”

Where Did the Number “1.96” Come From?

A detailed mathematical answer to that question is beyond the scope of this book, but here is the basic idea.

We assume that the population data is "normally distributed," meaning it would form a "normal curve" if we could test every individual or property within the population This normal curve resembles the outline of the Liberty Bell located in Philadelphia, Pennsylvania It is characterized by its "symmetric" shape, where folding it in half would allow one side to perfectly align with the other For a comprehensive understanding of the normal curve, refer to Fitz-enz and Davison (2002).

In this article, we focus on determining the lower and upper limits of population data within the normal curve, ensuring that 95% of the area under the curve falls between these limits For research studies involving more than 40 participants, these limits can be calculated as plus or minus 1.96 times the standard error of the mean (s.e.) from the sample This calculation is essential for establishing the confidence interval For further insights into this concept, readers are encouraged to refer to a reputable statistics textbook, such as Keller (2009).

The number 1.96 would change if we wanted to be confident of our results at a different level from 95 % as long as we have more than 40 people in our research study.

1 If we wanted to be 80 % confident of our results, this number would be 1.282.

In this book, we prioritize a 95% confidence level for our results, which is why we will consistently use the value of 1.96 in our research studies involving more than 40 participants.

You might be wondering if the value of 1.96 is always used in the confidence interval for the mean The answer is no, and we will clarify the reasons behind this shortly.

Finding the Value for t in the Confidence

Objective: To find the value for t in the confidence interval formula

The correct formula for the confidence interval about the mean for different sample sizes is the following:

To calculate a 95% confidence interval, first determine the sample mean (X) The upper limit is found by adding the product of the t-value and the standard error (s.e.) to the sample mean Conversely, the lower limit is calculated by subtracting the product of the t-value and the s.e from the sample mean The t-value can be obtained from the table provided in Appendix E of this book.

Objective: To find the value of t in the t-table in AppendixE

Before we get into an explanation of what is meant by “the value of t,” let’s give you practice in finding the value of t by using the t-table in AppendixE.

Keep your finger on Appendix Eas we explain how you need to “read” that table.

In this chapter, you will utilize the "confidence interval about the mean test," which requires finding the critical value of t for your research study To do this, refer to the first column on the left in Appendix E, labeled "sample size n."

To determine the value of t for your research study, locate the sample size in the first column of the table, then move to the right to find the corresponding value of t in the "critical t column," which is used for a 95% confidence interval about the mean For instance, if your study includes 14 participants, the t value is 2.160.

If you have 26 people in your research study, the value of t is 2.060.

If you have more than 40 people in your research study, the value of t is always 1.96.

The "critical t column" in Appendix E indicates the t value necessary to achieve 95% confidence in the significance of your statistical results This book operates under the assumption that you aim for a 95% confidence level in your statistical tests Consequently, the t value found in the t-table of Appendix E is essential for calculating the 95% confidence interval around the mean.

To calculate the confidence interval for the mean using Excel, first determine the value of t relevant to your sample size and desired confidence level Next, input your data into Excel and use functions such as AVERAGE and STDEV to compute the mean and standard deviation Finally, apply the formula for the confidence interval, incorporating the t-value, to derive the upper and lower bounds, ensuring accurate results for your statistical analysis.

Using Excel ’ s TINV Function to Find the Confidence

Objective: To use the TINV function in Excel to find the confidence interval about the mean

When you use Excel, the formulas for finding the confidence interval are:

Lower limit:ẳXTINVð10:95,n1ị*s:e:ðno spaces between these symbolsị ð3:3ị

Upper limit:ẳXỵTINVð10:95,n1ị*s:e:ðno spaces between these symbolsị ð3:4ị

In Excel formulas, the asterisk symbol (*) indicates multiplication, representing the concept of "times" in mathematical terms As mentioned in Chapter 1, 'n' denotes the sample size, while 'n1' refers to the sample size decreased by one.

In Chapter 1, we learned that the standard error of the mean (s.e.) is calculated by dividing the standard deviation (STDEV) by the square root of the sample size (n) To illustrate this concept, we will use Excel to determine the 95% confidence interval for the mean in a sample problem.

To evaluate whether the average time to fill a position, defined as the number of days from the delivery of an approved application to the acceptance of a job offer, has been 35 days over the past year, we will use this 35-day figure as our reference value.

To verify the validity of the claim, you gather relevant research data and employ a confidence interval analysis to evaluate the mean, ensuring a robust statistical assessment of your findings.

Using Excel to Find the 95 % Confidence Interval

Objective: To analyze the data using a 95 % confidence interval about the mean

In a recent research study, a random sample of acceptances from the past 12 months was analyzed to determine the TIME TO FILL for applicants The findings, illustrated in Fig 3.1, highlight the duration it took to complete the hiring process during this timeframe.

To analyze your data effectively, create a spreadsheet in Excel and utilize the following cell references to calculate the sample size (n), mean, standard deviation (STDEV), and standard error of the mean (s.e.) This process will provide you with essential statistical insights into your dataset.

B5: “How many days does it take between the delivery of an approved

B6: job requisition for staffing and the date on which an applicant accepts B7: the job offer?”

Enter the other TIME TO FILL data in cells A11:A29

Fig 3.1 Worksheet Data for TIME TO FILL (Practical Example)

Now, highlight cells A10:A29 and format these numbers in number format (zero decimal places) Center these numbers in Column A.

Fig 3.2 Example of TIME TO FILL Format for the Confidence Interval About the Mean Labels

B29: Draw a picture below this confidence interval

B32: lower (right-align this word)

B33: limit (right-align this word)

C31: ‘ - (note the single quotation mark at the beginning)

D31: ‘ -35 (note that you need to begin cell D31 with asingle quotation mark(‘) to tell Excel that this is alabel, and not a number)

F31: ‘ -– (note the single quotation mark)

D32: ref (right-align this word)

D33: value (right-align this word)

E32: Mean (right-align this word)

Now, align the labels underneath the picture of the confidence interval so that they look like Fig.3.3.

Next, name the range of data from A10:A29 as: TIME

D10: Use Excel to find the sample size

D13: Use Excel to find the mean

D16: Use Excel to find the STDEV

D19: Use Excel to find the s.e.

Now, you need to find the lower limit and the upper limit of the 95 % confidence interval for this study.

To achieve a 95% confidence level in your results, you can utilize Excel's TINV function The formula for calculating the lower limit of the confidence interval is essential for this process.

Fig 3.3 Example of Drawing a Picture of a Confidence Interval About the Mean Result

Note that this TINV formula uses 19 since 19 is one less than the sample size of

20 (i.e., 19 is n1) Note that D13 is the mean, while D19 is the standard error of the mean The above formula gives thelower limit of the confidence interval, 33.99.

The calculated upper limit of the confidence interval is 37.41 To ensure accuracy, format the mean, standard deviation, standard error of the mean, and both the lower and upper limits of your confidence interval to two decimal places in your Excel spreadsheet The resulting confidence interval is illustrated in Fig 3.4.

Fig 3.4 Result of Using the TINV Function to Find the Confidence Interval About the Mean

Note that you have drawn a picture of the 95 % confidence interval beneath cell B29, including the lower limit, the upper limit, the mean, and the reference value of

Now, let’s write the conclusion to your research study on your spreadsheet:

B35: Since the reference value of 35 days is inside the confidence

B36: interval, we accept that the TIME TO FILL a job acceptance

B37: for an approved requisition for staffing was 35 days last year.

When formatting your spreadsheet, it's essential to place the conclusion on three separate lines instead of one long line This approach prevents two issues: first, if you reduce the page layout to fit everything on one page, the font size will become too small to read; second, printing without reducing the layout may cause part of the conclusion to spill onto a separate page, compromising the professional appearance of your spreadsheet.

Your research study accepted the claim that the TIME TO FILL a job acceptance for an approved requisition for staffing during the past 12 months was 35 days (See Fig.3.5).

Save your resulting spreadsheet as: FILL3

Hypothesis Testing

Hypotheses Always Refer to the Population That

The first step is to understand that our hypotheses always refer to thepopulationof people or events in a study.

To evaluate the overall performance of Master's students in the Human Resource Management program, we can conduct in-depth interviews with a randomly selected sample of students two months prior to their graduation The insights gained from this sample will enable us to generalize our findings to the entire population of students set to graduate in the same timeframe.

The focus of our study is on the students who are set to graduate from the program in two months, representing the population of interest The specific students interviewed form our sample, which is a subset of this population Since sample sizes usually encompass only a fraction of the larger group, we aim to determine how the findings from our sample can be generalized to the entire population of graduating students.

That is why our hypotheses always refer to the population, and never to the sample of people or events in our study.

You will recall from Chap.1that we used the symbol:ð ịX to refer to the mean of the sample we use in our research study (See Sect.1.1).

We will use the symbol:μ(the Greek letter “mu”) to refer to the population mean.

In testing our hypotheses, we are trying to decide which one of two competing hypothesesabout the population meanwe should accept given our data set.

The Null Hypothesis and the Research (Alternative)

These two competing hypotheses are called thenull hypothesisand the research hypothesis.

Statistics textbooks typically refer to thenull hypothesiswith the notation:H0.

Theresearch hypothesisis typically referred to with the notation:H1, and it is sometimes called thealternative hypothesis.

Let’s explain first what is meant by the null hypothesis and the research hypothesis:

(1) The null hypothesis is what we accept as true unless we have compelling evidence that it is not true.

(2) The research hypothesis is what we accept as true whenever we reject the null hypothesis as true.

In the American legal system, individuals are presumed innocent until proven guilty by a jury, reflecting the principle of the null hypothesis, which posits that the defendant is innocent Conversely, the research hypothesis asserts that the defendant is guilty.

In Missouri, the state slogan "Show me" reflects the residents' skepticism and insistence on evidence over mere words This phrase signifies that Missourians prioritize actions over claims, believing that true intentions and honesty are demonstrated through behavior rather than spoken promises.

In hypothesis testing, the objective is to determine which of the two competing statements—the null hypothesis or the research hypothesis—can be accepted as true, given that both cannot coexist simultaneously.

In human resource management research, surveys frequently utilize rating scales to assess individuals' attitudes towards organizational activities Commonly employed scales include 5-point, 7-point, and 10-point formats, although various other scale values may also be used.

3.2.2.1 Determining the Null Hypothesis and the Research Hypothesis

When Rating Scales Are Used

This article provides examples of testing both the null hypothesis and research hypothesis using rating scales, demonstrating practical applications for these methods in a professional setting.

The Society for Human Resource Management (SHRM) is recognized as the largest association dedicated to human resource management, boasting over 250,000 members across more than 140 countries, all engaged in various aspects of the HR profession.

HR settings SHRM has more than 575 local chapters in the USA alone SHRM holds an Annual Conference and Exposition every year.

A 7-point scale can effectively gather feedback from participants regarding the value of the SHRM's annual international conference This feedback can be obtained through an email survey sent to attendees after the conference concludes.

So, how do we decide what to use as the null hypothesis and the research hypothesis whenever rating scales are used?

Objective: To decide on the null hypothesis and the research hypothesis whenever rating scales are used.

In order to make this determination, we will use a simple rule:

Rule: Whenever rating scales are used, we will use the “middle” of the scale as the null hypothesis and the research hypothesis.

In the above example, since 4 is the number in the middle of the scale (i.e., three numbers are below it, and three numbers are above it), our hypotheses become:

If the statistical test shows that the population mean for the attitude scale item is approximately 4, we conclude that we accept the null hypothesis This indicates that SHRM conference participants felt neutral, neither satisfied nor dissatisfied, regarding the overall quality of the conference.

If our statistical test reveals that the population mean significantly differs from 4, we reject the null hypothesis and accept the research hypothesis.

Fig 3.6 Example of a Rating Scale Item for a SHRM Conference (Practical Example)

Participants of the SHRM conference expressed high levels of satisfaction with the overall quality of the event, as evidenced by a sample mean that significantly exceeded the expected population mean of 4.

Participants at the SHRM conference expressed considerable dissatisfaction with the overall quality, as evidenced by a sample mean that was significantly lower than the anticipated population mean of 4.

Both of these conclusions cannot be true We accept one of the hypotheses as

“true” based on the data set in our research study, and the other one as “not true” based on our data set.

In a research study, the primary responsibility of the researcher is to determine whether to accept the null hypothesis or the research hypothesis as true based on the provided data set.

Let’s try some examples of rating scales so that you can practice figuring out what the null hypothesis and the research hypothesis are for each rating scale.

In the spaces in Fig.3.7, write in the null hypothesis and the research hypothesis for the rating scales:

Fig 3.7 Examples of Rating Scales for Determining the Null Hypothesis and the Research Hypothesis

Here are the answers to these three questions:

1 The null hypothesis is μ ẳ 3, and the research hypothesis is μ 6ẳ 3 on this 5-point scale (i.e the “middle” of the scale is 3).

2 The null hypothesis is μ ẳ 4, and the research hypothesis is μ 6ẳ 4 on this 7-point scale (i.e., the “middle” of the scale is 4).

3 The null hypothesis isμ ẳ 5:5, and the research hypothesis isμ 6ẳ 5:5 on this 10-point scale (i.e., the “middle” of the scale is 5.5 since there are 5 numbers below 5.5 and 5 numbers above 5.5).

Webster University, located in St Louis, Missouri, USA, conducts student evaluations through a Course Feedback form at the conclusion of all its courses, catering to over 21,000 students across 61 cities.

The Course Feedback form, utilized across 9 countries, comprises 12 rating items that assess course planning, organization, and the communication quality between instructors and students After course completion, the ratings are compiled and shared with instructors to enhance future teaching effectiveness Each item is evaluated using a 4-point scale.

In this study, the null hypothesis posits that the mean (μ) is equal to 2.5, while the research hypothesis suggests that the mean is not equal to 2.5 This is based on the observation that there are two ratings below and two ratings above 2.5 on the scale, which is designed such that lower scores indicate better outcomes, similar to scoring in golf.

Now, let’s discuss the 7 STEPS of hypothesis testing for using the confidence interval about the mean.

The 7 Steps for Hypothesis-Testing Using

the Confidence Interval About the Mean

Objective: To learn the 7 steps of hypothesis-testing using the confidence interval about the mean

There are seven basic steps of hypothesis-testing for this statistical test.

3.2.3.1 STEP 1: State the Null Hypothesis and the Research Hypothesis

When utilizing numerical scales in surveys, it's essential to recognize that both the null and research hypotheses pertain to the midpoint of the scale For instance, in a 7-point scale ranging from 1 (poor) to 7 (excellent), these hypotheses would specifically focus on the central value of the scale.

3.2.3.2 STEP 2: Select the Appropriate Statistical Test

In this chapter we are studying the confidence interval about the mean, and so we will select that test.

3.2.3.3 STEP 3: Calculate the Formula for the Statistical Test

You will recall (see Sect 3.1.5) that the formula for calculating the confidence interval about the mean is:

We discussed the procedure for computing this formula for the confidence interval about the mean using Excel earlier in this chapter The steps involved in using that formula are:

1 Use Excel’sẳCOUNT function to find the sample size.

2 Use Excel’sẳAVERAGE function to find the sample mean,X

3 Use Excel’sẳSTDEV function to find the standard deviation, STDEV.

4 Find the standard error of the mean (s.e.) by dividing the standard deviation (STDEV) by the square root of the sample size, n.

5 Use Excel’s TINV function to find the lower limit of the confidence interval.

6 Use Excel’s TINV function to find the upper limit of the confidence interval.

3.2.3.4 STEP 4: Draw a Picture of the Confidence Interval About the Mean, Including the Mean, the Lower Limit of the Interval, the Upper Limit of the Interval, and the Reference Value Given in the Null Hypothesis, H 0 (We Will Explain Step 4 Later in the Chapter).

3.2.3.5 STEP 5: Decide on a Decision Rule

(a) If the reference value is inside the confidence interval, accept the null hypothesis, H0

(b) If the reference value is outside the confidence interval, reject the null hypothesis, H0, and accept the research hypothesis, H1

3.2.3.6 STEP 6: State the Result of Your Statistical Test

When utilizing the confidence interval for the mean, there are two potential outcomes, but only one can be deemed "true." Therefore, your findings will ultimately reflect one of these two results.

Either: Since the reference value is inside the confidence interval, we accept the null hypothesis, H0

Or: Since the reference value is outside the confidence interval,we reject the null hypothesis, H0, and accept the research hypothesis, H1

3.2.3.7 STEP 7: State the Conclusion of Your Statistical Test in Plain

Summarizing the results of your statistical test in clear and concise language can be challenging, especially when aiming to make the conclusions understandable for individuals without a background in statistics, such as your boss This task requires careful consideration to ensure accuracy while maintaining simplicity Throughout this book, we will provide ample opportunities for you to practice this crucial skill.

Objective: To write the conclusion of the confidence interval about the mean test

Let’s set some basic rules for stating the conclusion of a hypothesis test.

Rule #1: Whenever you reject H0 and accept H1, you must use the word

“significantly” in the conclusion to alert the reader that this test found an important result.

Rule #2: Create an outline in words of the “key terms” you want to include in your conclusion so that you do not forget to include some of them.

Rule #3:Write the conclusion in plain English so that the reader can understand it even if that reader has never taken a statistics course.

Let’s practice these rules using the TIME TO FILL Excel spreadsheet that you created earlier in this chapter (FILL3), but first we need to state the hypotheses.

To assert that the average time to fill positions for job applicants who accepted offers in the past year was 35 days, the organization must establish specific hypotheses.

The reference value of 35 days falls within the 95% confidence interval for the mean of your data, leading us to accept the null hypothesis (H0) that the average time to fill over the past 12 months was indeed 35 days.

Objective: To state the result when you accept H 0

Result: Since the reference value of 35 days is inside the confidence interval, we accept the null hypothesis, H0.

Let’s try our three rules now:

Objective: To write the conclusion when you accept H 0

In this chapter, we adhere to a fundamental guideline: if the reference value falls within the confidence interval, we must avoid using the term "significantly" in our conclusions This rule is consistently applied to all problems discussed in this section.

Rule #2: The key terms in the conclusion would be:

– a job acceptance for an approved requisition from staffing

Rule #3: The average TIME TO FILL a job acceptance for an approved requisition from staffing during the past 12 months was 35 days.

Writing a conclusion when accepting the null hypothesis (H0) is straightforward, as it simply reiterates the statement made in the null hypothesis Conversely, crafting a conclusion upon rejecting H0 and accepting the alternative hypothesis (H1) is more complex To enhance understanding, we will practice formulating such conclusions through three illustrative case examples.

Objective: To write the result and conclusion when you reject H 0

In a recent time and motion study conducted by the organization, it was found that the average time taken to complete a specific laboratory procedure is 25 minutes This finding serves as the basis for formulating hypotheses regarding the efficiency and effectiveness of the procedure.

Suppose that your research yields the following confidence interval:

19 21 23 25 lower Mean upper Ref. limit limit Value

Result: Since the reference value is outside the confidence interval, we reject the null hypothesis and accept the research hypothesis

The three rules for stating the conclusion would be:

Rule #1: We must include the word “significantly” since the reference value of

25 is outside the confidence interval.

Rule #2: The key terms would be:

– average time needed to complete the procedure

– either “more than” or “less than”

Rule #3: The average laboratory time needed to complete this procedure was significantly less than 25 minutes, and it was probably closer to

The study concluded that the procedure was completed in an average of 21 minutes, significantly less than the 25-minute benchmark However, simply stating "significantly less than 25 minutes" is insufficient, as it fails to specify the exact difference between the sample mean and the 25-minute threshold.

To make the conclusion clear, you need to add: “probably closer to 21 minutes” since the sample mean was only 21 minutes.

Cost per hire is a crucial budgeting metric for organizations, enabling them to manage recruitment expenses effectively Financial officers can estimate this cost by analyzing a random sample of new hires from the past year It's essential to differentiate between the cost per hire for external candidates and those promoted internally Focusing on internal costs, organizations should consider various factors such as internal advertising, travel, referral bonuses, relocation expenses, and recruiter fees For instance, if an organization has set an average internal cost per hire at $4,000, tracking these expenses can help maintain budgetary control and optimize hiring processes.

You want to practice your data interpretation skills on the hypothetical data which produces the confidence interval below:

The hypotheses for this test would be:

The null hypothesis posits that the average cost of the hiring process is $4,000 If the sample's average cost does not significantly differ from this value, it supports the assumption that the true cost remains at $4,000.

Suppose that your analysis produced the following confidence interval for this test:

$3,400 $3,600 $3,800 $4000 lower Mean upper Ref. limit limit Value

Result: Since the reference value is outside the confidence interval, we reject the null hypothesis and accept the research hypothesis.

Rule #1: You must include the word “significantly” since the reference value is outside the confidence interval

– average INTERNAL COST PER HIRE

– applicants hired who were already working for the organization – during the past year

– less than or greater than (depending on the confidence interval) – significantly

– budgeted cost of $4,000 per hire

– and is probably closer to

In the past year, the average internal cost per hire for employees transitioning to different roles within the organization was notably lower than the budgeted figure of $4,000, estimated to be around $3,600.

Note that you need to use the word “less” since the sample mean of $3,600 was less than the reference value of $4,000.

The American Society for Training and Development (ASTD) offers comprehensive training programs aimed at enhancing the knowledge, skills, and credibility of HR professionals To assess the impact of their professional relationships, ASTD plans to survey its members, asking them to evaluate the significance of these connections on their career paths Members will rate their opinions on a scale from Strongly Disagree (1) to Agree.

2, Neutral is scored as 3, Agree is scored as 4, and Strongly Agree is scored as 5.

Suppose that you have been asked to use your Excel skills to determine the opinion of the sampled members.

Suppose that your research produced the following confidence interval for this survey item:

Result: Since the reference value is outside the confidence interval, we reject the null hypothesis and accept the research hypothesis

The three rules for stating the conclusion would be:

Rule #1: You must include the word “significantly” since the reference value is outside the confidence interval

– important to their career paths

Rule #3: The sample of members of ASTD significantly agreed that the professional relationships they developed through ASTD membership have been important to their career paths.

In this context, it is essential to convey the conclusion without relying on specific numerical references, allowing for a clearer and more focused summary of the findings Emphasizing the overall implications rather than exact figures can enhance understanding and engagement.

If you want a more detailed explanation of the confidence interval about the mean, see Zikmund and Babin (2010).

Alternative Ways to Summarize the Result

The 7 STEPS for Hypothesis-Testing Using

The 9 STEPS for Hypothesis-Testing Using

Tiêu đề	Excel 2013 for Human Resource Management Statistics A Guide to Solving Practical Problems
Tác giả	Thomas J. Quirk, Julie Palmer-Schuyler
Người hướng dẫn	Thomas J. Quirk
Trường học	Springer International Publishing
Chuyên ngành	Human Resource Management Statistics
Thể loại	guide
Năm xuất bản	2016
Thành phố	Switzerland

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Số trang	265
Dung lượng	11,15 MB