The manager of a newly opened book store wants to estimate the average expenditure of his customers using a confidence interval. He estimates that the population standard deviation is approximately $23.50. (a) For a 99% confidence level, find the appropriate sample size necessary to achieve a margin of error of 4.50. Determine z; = Round your answer (:1) UP to the next whole number. The required sample size n is (b) For a 90% confidence level, find the appropriate sample size necessary to achieve a margin of error of 4.50. Determine z; = Round your answer (:1) UP to the next whole number. The required sample size n is (c) Compare parts (a) and (b). Select the correct statement. 0 If the confidence level decreases, then the required sample size also decreases. 0 If the confidence level decreases, then the required sample size increases. 0 If the confidence level decreases, then the required sample size does not change. (d) Suppose that the confidence level remains invariant. How should we change the sample size to achieve the larger confidence interval? 0 Increase the sample size. 0 Decrease the sample size. 0 Do nothing as the length of the confidence interval does not depend on the sample size