Question: Continue with Exercise, and suppose that the survey is to estimate two characteristics of the university students. One characteristic is thought to have a prevalence of roughly 50% of the population and the other only 10%. For each of the following conditions, find the sample size required.
a. Both estimates are to be accurate to about 1% (i.e., the standard error of each estimator should be at most 1%).
b. Each statistic is to be accurate to about 1/10 of its population parameter.
Exercise: Suppose a survey of the 32,000 students at a university is planned. The goal of the survey is to estimate the percentage of the students who own PCs. Find the minimum sample size required to make a 95% confidence interval for the population percentage that is at most 4 percentage points wide. The variance of the population is unknown. Ignore the finite population correction factor.
a. In your calculation of the sample size use the percentage of students who own PCs in the survey of the statistics class to estimate the population variance for the university students.
b. Instead of using the percentage from the statistics class sample in your calculation, assume the worst-case scenario - that is, the largest variance possible for the parameter.