Question

The 40-hour work week did not become a U.S. standard until 1940. Today, many white-collar employees work more than 45 hours per week because management demands longer hours or offers large monetary incentives. A random sample of 28 white-collar employees worked on average 46.80 hours per week. Is there any evidence that the true mean number of hours worked per week by white-collar employees is greater than 45? Assume that the population standard deviation is 3.04 hours. Please use the exact value (from R) for all critical values.

a) What assumptions are required so that you can perform a hypothesis tests and confidence interval for the mean hours worked per week?

b) Should you use a z distribution or a t distribution in this problem? Note that you will only get one try to get this question correct.

Please explain the correct choice.

c) Is there any evidence to suggest the true mean number of hours worked per week by white-collar workers is greater than 45? Perform the hypothesis test at a 0.7% significance level.

Calculate the test statistic.

Calculate the p-value. Please write your answer in scientific notation using an E for the exponent and including at least 3 decimal places. For example, 1.234 x 10^-5 would be written as 1.234E-5

d) Calculate the appropriate 99.3% bound that is consistent with what you did in parts b) and c).

Interpret the bound calculated above.

e) In practical terms, do you think that the number of hours worked per week by white-collar workers is greater than 45? To receive credit, your answer must be more than just repeating the conclusions in parts c) and d). Please explain your answer. Hint: Difference and Effect Size.

f) Explain why parts c) and d) state the same thing. That is, what in part c) is consistent with what in part d)?

Answer 1

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