The number of hours spent studying by students on a large campus in the week before final exams follows a normal distribution with a standard deviation of 8.4 hours. A random sample of these students is taken to estimate the population mean number of hours studying.
a) How large of a sample is needed to ensure that the probability that the sample mean differs from the population mean by more than 2.0 hours is less than 0.05?
b) Without doing the calculations, state whether a larger or smaller sample size compared to the sample size in part (a) would be required to guarantee that the probability of the sample mean differing from the population mean by more than 2.0 hours is less than 0.10.
c) Without doing the calculations, state whether a larger or smaller sample size compared to the sample size in part (a) would be required to guarantee that the probability of the sample mean differing from the population mean by more than 1.5 hours is less than 0.05.