Question

The mean length of a work week for the population of workers was reported to be
39.2 hours. Suppose that we would like to take a current sample of workers to see
whether the mean length of a work week has changed from the previously
reported 39.2 hours.
a. State the hypotheses that will help us determine whether a change occurred in
the mean length of a work week.
b. Suppose a current sample of 112 workers provided a sample mean of 38.5
hours. Use a population standard deviation σ = 4.8 hours. What is the p-
value?
c. At =0.05, can the null hypothesis be rejected? What is your conclusion
regarding the mean length of a work week?
d. Now suppose population standard deviation is not known and from the above
sample you calculate standard deviation to be 6 hours. Test the hypothesis
that the mean length of a work week has changed from the previously
reported 39.2 hours.

Answer 1

Ho: mean1 = mean2
Ha: mean1 ≠ mean2

Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion related to the Z score.