We would like to estimate the true mean amount of time (in minutes) Canadian teenagers spend on the internet per day. The population standard deviation of daily internet usage time is known to be 55 minutes.
(a) What sample size is required in order to estimate to within 15 minutes with 90% confidence?
(b) What sample size is required in order to estimate to within 5 minutes with 90% confidence?
(c) For a fixed confidence level, when we decrease the desired margin of error to one third its original value, how many times larger a sample size will be require?
(d) What sample size is required in order to estimate to within 15 minutes with 98% confidence?
(e) For a fixed margin of error, when we increase the desired confidence level, what happens to the required sample size? (increase, decrease or remain the same).
(f) The United States has ten times the population of Canada. Assuming equal standard deviations, how many American teenagers must be sampled in order to estimate the true mean amount of time American teenagers spend on the internet per day to within 15 minutes with 90% confidence?