Question

The Federal Government wants to determine if the mean number of business e-mails sent and received per business day by its employees differs from the mean number of e-mails sent and received per day by corporate employees, which is 101.5. Suppose the department electronically collects information on the number of business e-mails sent and received on a randomly selected business day over the past year from each of 10,163 randomly selected Federal employees. The results are provided in the file FedEmail. Test the Federal Government’s hypothesis at α = 0.01. Discuss the practical significance of the results.

Answer 1

The hypothesis being tested is:

H0: µ = 101.5

Ha: µ ≠ 101.5

The test statistic, z = (x - µ)/σ/√n

z = (100.47 - 101.5)/25/√10163

z = -4.15

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.01), we can reject the null hypothesis.

Therefore, we can conclude that the mean number of business e-mails sent and received per business day by its employees differs from the mean number of e-mails sent and received per day by corporate employees, which is 101.5.

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