The employees of a large international company would like to have vision care as part of their benefits package. A researcher needs to estimate the amount of money that employees and their beneficiaries spend on such treatment, on average. A sample of 784 employees reveals the mean amount spent last year was $1,009.44, with a standard deviation of $112.78. We assume that the population standard deviation is close to the last number. (a] Construct a 95% confidence interval for the population mean amount spent on vision care. Find =# Round the confidence interval values to 2 decimal places. What is the 95% confidence interval? (b) Construct a 98% confidence interval for the population mean amount spent on vision care. Find zam Round the confidence interval values to 2 decimal places. What is the 98% confidence interval?(c) What is not true about the confidence intervals? Olf the confidence level increases from 95% to 98%, then the length of the confidence does not change. O There is a 95% chance that the confidence interval constructed in part (a) contains the true population mean amount spent on vision care. O The researcher is 98% confident that the confidence interval constructed in part (b) contains the true average amount spent on vision care. O If the confidence level increases from 95% to 98%, then the confidence interval becomes longer.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 $21.00. (a) For a 98% confidence level, find the appropriate sample size necessary to achieve a margin of error of 4.50. Determine 29 = Round your answer (n) 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 zg = Round your answer (n) UP to the next whole number. The required sample size n is (c) Compare parts (a] and (b). Select the correct statement. If the confidence level decreases, then the required sample size does not change. O'If the confidence level decreases, then the required sample size also decreases, Off the confidence level decreases, then the required sample size increases, DOF(d) Suppose that the confidence level remains invariant. How should we change the sample size to achieve the larger confidence interval? O Decrease the sample size. O Increase the sample size. O Do nothing as the length of the confidence interval does not depend on the sample size