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 1024 employees reveals the mean amount spent last year was $757.03, with a standard deviation of $125.33. 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 z2=z2=

Round the confidence interval values to 2 decimal places.

What is the 95% confidence interval?

(b) Construct a 99% confidence interval for the population mean amount spent on vision care.

Find z2=z2=

Round the confidence interval values to 2 decimal places.

What is the 99% confidence interval?

(c) What is not true about the confidence intervals?

• If the confidence level increases from 95% to 99%, then the length of the confidence does not change.
• If the confidence level increases from 95% to 99%, then the confidence interval becomes longer.
• The researcher is 99% confident that the confidence interval constructed in part (b) contains the true average amount spent on vision care.
• There is a 95% chance that the confidence interval constructed in part (a) contains the true population mean amount spent on vision care.