A sample of 148 college students at a large university reports getting an average of 6.85 hours of sleep last night with a standard deviation of 2.12 hours.
a) Verify that it is reasonable to use the t-distribution to construct a confidence iterval for the average amount of sleep students at this university got last night.
b) Constuct a 98% confidence interval for the average amount of sleep students at this universit got last night. Use two decimal places in your margin of error. Also , use t* = 2.352
c) Provide an interpretation of your interval in the context of this data situation.
d) Suppose you want to conduct a similar study at your university. Assuming that the standard deviation of this sample is a reasonable estimate of the standard deviation of sleep time at your university, how many students do you need to survey to estimate the mean sleep time of students at your university with 95% confidence and a margin of error of 0.5 hours?