Question

The 40-hour work week did not become a U.S. standard until 1940. Today, many white-collar employees work more than 42 hours per week because management demands longer hours or offers large monetary incentives. A random sample of 22 white-collar employees worked on average 44.03 hours per week. Is there any evidence that the true mean number of hours worked per week by white-collar employees is greater than 42? Assume that the population standard deviation is 3.09 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 42? Perform the hypothesis test at a 0.8% significance level.

i) Calculate the test statistic.

ii) 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.

iii) Write the complete four steps of the hypothesis test below.

iv) Provide your computer code for part c) below.

d) Calculate the appropriate 99.2% bound that is consistent with what you did in parts b) and c).

i) Interpret the bound calculated above.

ii) Provide your computer code for part d) below.

e) In practical terms, do you think that the number of hours worked per week by white-collar workers is greater than 42? 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

given that

The 40-hour work week did not become a U.S. standard until 1940. Today, many white-collar employees

a) assumptions:

the sample is drawn using sample random sampling

the population from which the sample is drawn is approximately normal

sample are independent

b) as population standard deviation is known we use z- distribution

c)

test statistic

p-value

p-value

reject

there is sufficient evidence to conclude that the true mean number of hours worked per week by white color workers as greater than 45.

d) for confidence level.

the 99% CI for true mean

the CI is

round is 4 decimal places.

the bound exceed the lower bound is greater than . this shows that the true mean is greater than . the bound is consistant with the conclusion in above part.thers is chance that the true mean lie within &

e) effect size contents of

, which shows medium effect. the mean difference is standard deviation.the shows that there is a moderate difference in actual mean and sample mean.which shows that mean hours of working is different from

f) part c and part d yield same conclusion because the significance level remains the same for both the parts .