Because the company is sampling the coffee production process every hour, there are 720 confidence intervals for the mean caffeine content m constructed every month.
a. If the level of confidence remains at 95% for the 720 confidence intervals in a given month, how many of the confidence intervals would you expect to fail to contain the value of m and hence provide an incorrect estimation of the mean caffeine content?
b. If the number of samples is increased from 50 to 100 each hour, how many of the 95% confidence intervals would you expect to fail to contain the value of m in a given month?
c. If the number of samples remains at 50 each hour but the level of confidence is increased from 95% to 99% for each of the intervals, how many of the 95% confidence intervals would you expect to fail to contain the value of µ in a given month?