Question: A corporation randomly selects 150 salespeople and finds that 66% who have never taken a self-improvement course would like such a course. The firm did a similar study 10 years ago in which 60% of a random sample of 160 salespeople wanted a self-improvement course. The groups are assumed to be independent random samples. Let π 1 and π 2 represent the true proportion of workers who would like to attend a self-improvement course in the recent study and the past study, respectively.

1. If the firm wanted to test whether this proportion has changed from the previous study, which represents the relevant hypotheses?
   1. H 0 : π 1 - π 2 = 0 versus H 1: π 1 - π 2 ≠ 0
   2. H 0 : π 1 - π 2 ≠ 0 versus H 1 : π 1 - π 2 = 0
   3. H 0 : π 1 - π 2 ≤ 0 versus H 1 : π 1 - π 2 > 0
   4. H 0 : π 1 - π 2 ≥ 0 versus H 1 : π 1 - π 2 < 0
2. What is the unbiased point estimate for the difference between the two population proportions? Explain how you obtain your answer.
3. What is/are the critical value(s) when performing a Z test on whether population proportions are different if α = 0.05? Explain how you obtain your answer.
4. What is the estimated standard error of the difference between the two sample proportions? Show how you obtain your answer.
5. Construct a 95% confidence interval estimate of the difference in proportion of workers who would like to attend a self-improvement course in the recent study and the past study. Show how you obtain your answer.
6. The company tests to determine at the 0.05 level whether the population proportion has changed from the previous study. Which would be the conclusion? Explain how you obtain your answer.

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