As part of a study of corporate employees, the director of human resources for P

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 35 Cincinnati employees showed they travel a mean of 370 miles per month. A sample of 40 Pittsburgh employees showed they travel a mean of 380 miles per month. The population standard deviations for the Cincinnati and Pittsburgh employees are 30 and 26 miles, respectively. At the 0.05 significance level, is there a difference in the mean number of miles traveled per month between Cincinnati and Pittsburgh employees? a. Is this a one-tailed or a two-tailed test? O One-tailed test O Two-tailed test b. State the decision rule. (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) The decision rule is to reject H0pC P if z is the interval ( c. Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) Value of the test statistic

Explanation / Answer

The statistical software output for this problem is:

Two sample Z summary hypothesis test:
1 : Mean of population 1 (Std. dev. = 30)
2 : Mean of population 2 (Std. dev. = 26)
1 - 2 : Difference between two means
H0 : 1 - 2 = 0
HA : 1 - 2 0

Hypothesis test results:

Hence,

a) Two tailed Test

b) Decision Rule: Reject Ho if z is outside the interval (-1.96, 1.96)

c) Test statistic = -1.53

d) Do not reject Ho.

Difference n1 n2 Sample mean Std. err. Z-stat P-value 1 - 2 35 40 -10 6.5279618 -1.5318717 0.1256

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