Statistical inference for the population proportion
To find the effect of a recent policy change on employee morale, a large corporation decides to conduct an opinion survey, asking N randomly selected employees whether they are satisfied with the new policy.
- How many employees must be sampled in order to guarantee a sampling error (95% confidence interval) within +/- 2%?
- A survey is conducted, using the value of N chosen in part a. This survey reveals that 62.5% of the sampled employees are satisfied with the new policy. What is the 95% confidence interval for p, the proportion of all company employees that are satisfied with the new policy? What is the 99% confidence interval for p?
- Is the sample evidence sufficient to conclude that more than 60% of employees are satisfied with the new policy? To answer this question, perform a hypothesis test at α = .05. State the alternative and null hypotheses, compute the observed significance level (p-value), and state the conclusion of your test.
- What are the potential effects of Type I and Type II errors for this hypothesis test? How would the proportions of these errors be changed if you were to use a lower value of α, such as α = .01, instead of α = .05?