We would like to estimate the true mean annual electricity usage by all Canadian homes. Suppose that annual electricity usage follows a normal distribution with standard deviation1526kilowatt hours (kWh).

(a) What sample size is required to estimate the true meanannual electricity usage to within400 kWhwith95% confidence?

(b) What sample size is required to estimate the true mean annual electricity usage to within100 kWhwith95% confidence?

(c) For a given confidence level, how many times larger a sample size is required when we divide the desired margin of error by four?

(d)Usingonlythe result from (a), what sample size would be required to estimate the true mean annual electricity usage towithin 800 kWh with95% confidence?

(e) What sample size is required to estimate the true meanannual electricity usage to within 400 kWh with99% confidence?

(f) Comparing the results from (a) and (e), what happens to the required sample size when weincrease the confidence level? (Does it increase or decrease?)