8 - 4/17/2011 www.lecturebook.com/homeworks/sho Assignm ent...

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Assignment Stats 250 W11 HW 8 Graded Point Total: 26 out of 30 a. 4 out of 4 points State the null and alternative hypotheses for testing whether or not the training level has an effect on the mean time. Clearly indicate the description of these three parameters of interest for the hypotheses in the space provided. H 0 : _________________________ versus H a : _________________________________________ where ______ = ______________________________________________________________________ ______ = ______________________________________________________________________ ______ = ______________________________________________________________________ Your Answer: Required Assignment Stats 250 W11 HW 8 Question 1 (Chapter 16) A supervisor wants to study the relationship between employee training and time required to complete a job- related task. Three levels of employee training are considered: Beginner, Intermediate, and Advanced. Thirty new employees were randomly selected and each employee was randomly assigned to one of the three training levels. After the training was complete, the time (in minutes) it takes each employee to complete the task is recorded. Descriptive statistics and ANOVA results from SPSS are given below. The data set is time.sav . Descriptives Time N Mean Std. Dev. Std. Error 95% Confidence Interval for Mean Minimum Maximum Lower Bound Upper Bound 1 = Beginner 10 46.90 5.322 1.683 43.09 50.71 39 58 2 = Intermediate 43.20 6.563 2.075 38.51 47.89 33 53 3 = Advanced 28.80 4.541 1.436 35.55 42.05 31 46 Total 30 42.97 6.316 1.153 40.61 45.33 4/17/2011 www.lecturebook.com/homeworks/sho… lecturebook.com/homeworks/show/47 1/11
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Ho: μ 1= μ 2= μ 3 versus Ha: at least one μ i is different where μ 1 = population mean amount of time for all employees after going through a beginner level training session to complete a job-related task. μ 2 = population mean amount of time for all employees after going through an intermediate level training session to complete a job-related task. μ 3 = population mean amount of time for all employees after going through an advanced level training session to complete a job-related task. Solution: H 0 : μ 1 = μ 2 = μ 3 vers us H a : At least one population mean is different where μ 1 = population mean time to complete task for all employees trained at beginner level; μ 2 = population mean time to complete task for all employees trained at intermed level; μ 3 = population mean time to complete task for all employees trained at advanced level. b. 2 out of 2 points Use SPSS to generate the ANOVA output for testing the above hypotheses. Copy the ANOVA table from SPSS output file and paste it into the textbox below. Use the F statistic and p- value to answer part (d). Your Answer: t ANOVA Time Sum of Squares df Mean Square F Sig. Between Groups 328.867 2 164.433 5.361 .011 4/17/2011 www.lecturebook.com/homeworks/sho… lecturebook.com/homeworks/show/47 2/11
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Within Groups 828.100 27 30.670 Total 1156.967 29 Solution: t ANOVA Time Sum of Squares df Mean Square F Sig. Between Groups 328.867 2 164.433 5.361 .011 Within Groups 828.100 27 30.670 Total 1156.967 29 c. 1 out of 1 points The ANOVA table gives the test statistic. What is the distribution of the observed test statistic (if we assume that, on average, the time required to complete the task will be similar across training levels)? Be specific.
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This note was uploaded on 01/26/2012 for the course STATS 250 taught by Professor Gunderson during the Winter '10 term at University of Michigan.

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8 - 4/17/2011 www.lecturebook.com/homeworks/sho Assignm ent...

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