As part of a study of corporate employees, the director of human resources for P
ID: 3134813 • Letter: A
Question
As part of a study of corporate employees, the director of human resources for PNC, Inc., wants to compare the distance traveled to work by employees at its office in downtown Cincinnati with the distance for those in downtown Pittsburgh. A sample of 45 Cincinnati employees showed they travel a mean of 390 miles per month. A sample of 40 Pittsburgh employees showed they travel a mean of 400 miles per month. The population standard deviation for the Cincinnati and Pittsburgh employees are 30 and 26 miles, respectively. At the .02 significance level, is there a difference in the mean number of miles traveled per month between Cincinnati and Pittsburgh employees?
a. State the appropriate null and alternative hypotheses. (Show all work)
b. Calculate the test statistic. (Show all work)
c. Determine the critical value assuming an a = 0.02. (Show all work)
d. Should you reject the null hypothesis?—Provide a basis for your decision. Is there a difference in the mean number of miles traveled per month between Cincinnati and Pittsburgh employees? (Show all work)
Explanation / Answer
H0: mu1 = mu2
Ha: mu1 not equal to mu2
Two tailed test
Alpha = 0.02
Group Group One Group Two
Mean 45.00 40.00
SD 30.00 26.00
SEM 1.52 1.30
N 390 400
t = 2.5052
df = 788
standard error of difference = 1.996
p value = 0.0124
As p <0.02, reject that two means are equal
They are different at 2% significance.
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