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 400 employees reveals the mean amount spent last year was $976.65, with a standard deviation of $1 1 1.34. We assume that the population standard deviation is close to the last number. (a) Construct a 90% confidence interval for the population mean amount spent on vision care. '2 Round the confidence interval values to 2 decimal places. What is the 90% confidence interval? - (b) Construct a 99% confidence interval for the population mean amount spent on vision care. 2 ' k J Round the confidence interval values to 2 decimal places. What is the 99% confidence interval? [ Jamel (c) What is not true about the confidence intervals? 0 If the confidence level increases from 90% to 99%, then the confidence interval becomes shorter. 0 If the confidence level increases from 90% to 99%, then the confidence interval becomes longer. 0 The researcher is 99% confident that the confidence interval constructed in part (b) contains the true average amount spent on vision care. 0 There is a 90% chance that the confidence interval constructed in part (a) contains the true population mean amount spent on vision care