THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION

Essay

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of hours spent studying by students on Michigan State campus in the week before final exams follows a normal distribution with standard deviation 9.5 hours.A random sample of these students is taken to estimate the population mean number of hours studying.
-Without doing the calculations,state whether a larger or smaller sample would be required to guarantee that the probability that the sample mean differs from the population mean by more than 1.8 hours is less than 0.05,when compared to the sample needed to ensure that the probability that the sample mean differs from the population mean by more than 2.1 hours is less than 0.05.