Question

Salaried workers at a large corporation receive 2 weeks’ paid vacation per year. Sixteen randomly selected workers from this corporation were asked whether or not they would be willing to take a 3% reduction in their annual salaries in return for 2 additional weeks of paid vacation. The following are the responses of those workers:

No   Yes No   No   Yes   No   No Yes Yes   No   No   No   Yes   No   No   No

a. What is the point estimate for the proportion of all workers that would accept a 3% pay reduction in return for 2 additional weeks of paid vacation?
b. Construct a 97% confidence interval for the proportion of workers that would accept a 3% pay reduction in return for 2 additional weeks of paid vacation based on this sample.
c. If the corporation wanted the margin of error for the proportion to be 0.10 (with 97% confidence), what sample size would you tell them to collect?
d. Test the hypothesis that the proportion of all workers that would accept a 3% pay reduction in return for 2 additional weeks of paid vacation is equal to 50%, using a significance level of .10.

Answer 1

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