SOLUTION: You are the Vice President for Human Resources at XYZ Investment Management, Inc. Your employees have recently complained about their long working hours. You collected a sample o

Question 134429: You are the Vice President for Human Resources at XYZ Investment Management, Inc. Your employees have recently complained about their long working hours. You collected a sample of 25 weekly timesheets and calculated an average of 41.5 hours with a standard deviation of 2.5 hours.
Over lunch, you discuss this problem with your long-time college friend working for Bayview Financial. She points out that in her company, the employees work an average of 42 hours. The data that she recently collected included timesheets for 35 employees. She calculated a standard deviation of 3.
1. Which test do you have to use in order to answer the question: �Do the employees at XYZ Investment Management on average work fewer hours than the employees at Bayview Financial?�
Please circle the correct answer:
A. Two-sample test of means (large sample)
B. Two-sample test of means (small sample)
C. T-test of one mean
D. Two sample test of proportions
2. Please state your hypotheses, H0 and Ha, and perform the hypothesis test using the 5-step testing procedure [alpha = 0.05].

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
You are the Vice President for Human Resources at XYZ Investment Management, Inc. Your employees have recently complained about their long working hours. You collected a sample of 25 weekly timesheets and calculated an average of 41.5 hours with a standard deviation of 2.5 hours.
Over lunch, you discuss this problem with your long-time college friend working for Bayview Financial. She points out that in her company, the employees work an average of 42 hours. The data that she recently collected included timesheets for 35 employees. She calculated a standard deviation of 3.
1. Which test do you have to use in order to answer the question: �Do the employees at XYZ Investment Management on average work fewer hours than the employees at Bayview Financial?�
Please circle the correct answer:
A. Two-sample test of means (large sample)
Comment: Some textbook use a criteria of n>30 for "large".
If yours is that way the answer is "A"; if not, the answer is "B".
-------------------
B. Two-sample test of means (small sample)
C. T-test of one mean
D. Two sample test of proportions
-------------------
2. Please state your hypotheses, H0 and Ha, and perform the hypothesis test using the 5-step testing procedure [alpha = 0.05].
Ho: mu(xyz)-mu(bay) = 0
Ha: mu(xyz)-mu(bay) < 0
------------------------------
Critical value of one-tail z-test with alpha=5% is -1.645
--------------------
Test statistic:
z(41.5-42)= (-0.5)/[sqrt[(2.5^2/25)+(3^2/35)] = -0.7021
--------------------
Conclusion:
Fail to reject Ho since the test statistic is not less than the critical value.
-----------------------
Cheers,
Stan H.

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