In a sample survey of 68 high-tech companies, Culpepper and Associates reported that the average training budget per employee for companies in the sample was $894. If the sample was selected from a population of 1320 companies, and the standard deviation for the sample was $446,
a. Estimate the average training budget per employee for the population of high-tech firms represented here, using a 95% confidence interval.
b. Suppose you wanted to reduce the margin of error for the interval you produced in part a to $20, without sacrificing confidence. How big a sample size would you recommend?
c. For the situation described in part b, suppose the size of the population is actually 5463 companies, rather than 1320. Recommend the appropriate sample size.