One Sample T test - book

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Nov 24, 2024

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CHAPTER 5 The One-Sample tTest T he one-sample t test is used when the mean of one sample is compared to some known or estimated population mean. The sample is typically different from the population in some way, and the question of interest is whether the mean of the sample differs significantly from the mean of the pop ulation on a dependent variable of interest. An example of a one-sample t test is presented below. Example An industrial psychologist hired by a leading accounting firm wanted to know if the average num ber of hours worked per week at the firm was significantly different from the national average of 52 hours for accountants. The industrial psychologist randomly sampled 16 people from different divi sions within the firm and recorded the average number of hours they worked per week over a three month period. The dependent variable in this study is the number of hours worked per week. Objective and Data Requirements of the One-Sample t Test The One-Sample t Test Objective Data Requirements Example To determine whether the mean of a sample differs significantly from some known or estimated population mean. One sample of participants Accountants at leading accounting firm Dependent variable Dependent variable Continuous • Number of hours worked per week Null and Alternative Hypotheses The null hypothesis (HQ) states that the number of hours worked per week at the leading account ing firm is equal to the national average of 52 hours: H 0 - fx = 52 The alternative hypothesis (H\) states that the number of hours worked per week at the leading accounting firm is not equal to the national average of 52 hours: ^ : ix * 52 62
Chapter 5 / The One-Sample t Test 63 Evaluation of the NuLL Hypothesis The one-sample t test provides a test of the null hypothesis that the number of hours worked per week at the accounting firm is equal to 52 hours. If the t test produces results that seem unlikely if the null hypothesis is true (results that occur less than 5% of the time), then the null hypothe sis is rejected. If the t test produces results that seem fairly likely if the null hypothesis is true (results that occur greater than 5% of the time), then the null hypothesis is not rejected. Research Question The fundamental question of interest in a research study can also be expressed in the form of a research question, such as, "Is the number of hours worked per week for employees at a leading accounting firm different from the national average of 52 hours?" The Data The data for the 16 participants are presented in Figure 5.1. Participant 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Hours worked per week 54 48 68 53 60 45 57 62 71 60 55 63 68 64 56 60 Figure 5.1 The number of hours worked per week by the 16 employees at the leading accounting firm. (Note: The participant variable is included for illustration but will not be entered into SPSS.) Data Entry and Analysis in SPSS Steps 1 and 2 below describe how to enter the data in SPSS. The data file is also on the web at www.pearsonhighered.com/yockey under the name hours worked.sav in the Chapter 5 folder. If you prefer to open the file from the web site, skip to Step 3. Step 1: Create the Variable 1. Start SPSS. 2. Click the Variable View tab. In SPSS, one variable will be created for the number of hours worked per week by the employees at the leading accounting firm. The variable will be named hoursweek. 64 Unit II / Inferential Statistics
3. Enter the name hoursweek and press the down arrow key (I). See Figure 5.2 for details. • Untitled! [DataSetO] - PASW Statist! Data Trartstorfn Analyze Graphs LBiiies Adverts V*WGW Help n MI MM,J ^ 1. I hoursweek Numeric : gataView variable View ; h^ m ml Vidth Decimals Label Values Missing : Columns I Align 2 None :Nona 8 B Riant PASWStaii.fti':: erccessor BTeatfy : Role \ Input
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