An experiment has been conducted at a university to compare the mean number of study hours expended per week by student athletes with the mean number of hours expended by non-athletes. A random sample...

An experiment has been conducted at a university to compare the mean number of study hours expended per week by student athletes with the mean number of hours expended by non-athletes. A random sample of 55 athletes produced a mean equal to 20.6 hours studied per week and a standard deviation equal to 5.8 hours. A second random sample of 200 non-athletes produced a mean equal to 23.5 hours per week and a standard deviation equal to 4.6 hours. How many students would need to be sampled in order to estimate the difference in means to within 1.5 hours with probability 95%?