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 sam- ple mean to be 68.6 hours, with a standard deviation of 8.2 hours.
a. Using the sample data, construct a 99 percent confidence interval for the population mean.
b. Does the 99 percent confidence interval include the value suggested by the NCAA? Interpret this result.
c. Suppose you decided to switch from a 99 to a 95 percent confidence interval. Without performing any calculations, will the interval increase, decrease, or stay the same? Which f the values in the formula will change?