The National Collegiate Athletic Association (NCAA) reported that the mean number of hours spent per week on coaching and recruiting by college football assistant coaches during the season was 70. A random sample of 50 assistant coaches showed the sample mean to be 68.6 hours, with a standard deviation of 8.2 hours.
a. Using the sample data, construct a 99% confidence interval for the population mean.
b. Does the 99% confidence interval include the value suggested by the NCAA? Interpret this result.
c. Suppose you decided to switch from a 99% to a 95% confidence interval. Without performing any calculations, will the interval increase, decrease, or stay the same? Which of the values in the formula will change?