Homework SourseAs part of a study of corporate employees the director of hu
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 .05 significance level, is there a difference in the mean number of miles traveled per month between Cincinnati and Pittsburgh employees?
1. 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 H0:µC = µP if z is outside the interval (___, ____)
2. Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.)
the test statistic is z =
| 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 .05 significance level, is there a difference in the mean number of miles traveled per month between Cincinnati and Pittsburgh employees? 1. 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 H0:µC = µP if z is outside the interval (___, ____) 2. Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) the test statistic is z = |
Solution
1.
As this is a 2 tailed 0.05 level test, then by using table/technology, we reject Ho if it is outside the interval
(-1.96, 1.96) [ANSWER]
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2.
Formulating the null and alternative hypotheses,
Ho: u1 - u2 = 0
Ha: u1 - u2 =/ 0
At level of significance = 0.05
As we can see, this is a two tailed test.
Calculating the means of each group,
X1 = 370
X2 = 380
Calculating the standard deviations of each group,
s1 = 30
s2 = 26
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):
n1 = sample size of group 1 = 35
n2 = sample size of group 2 = 40
Also, sD = 6.527961835
Thus, the z statistic will be
z = [X1 - X2 - uD]/sD = -1.531871701 = -1.58 [ANSWER]
