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 deviation 1443 kilowatt hours (kWh).
(a) What sample size is required to estimate the true mean annual electricity usage to within 400 kWh with 96% confidence?
(b) What sample size is required to estimate the true mean annual electricity usage to within 100 kWh with 96% 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) Using only the result from (a), what sample size would be required to estimate the true mean annual electricity usage to within 800 kWh with 96% confidence?
(e) What sample size is required to estimate the true mean annual electricity usage to within 400 kWh with 99% confidence?
(f) Comparing the results from (a) and (e), what happens to the required sample size when we increase the confidence level?