Question: A furniture mover calculates the actual weight of a shipment as a proportion of estimated weight for a sample of 31 recent jobs. The sample mean is \(1.13\) and the sample standard deviation is .16.

a) Calculate a 95% confidence interval for the population mean using the t distribution.

b) Assume that the population standard deviation is known. Compute a 95% confidence interval.

c) Why is the second interval narrower? (I know it is a z distribution so you do not need to say that).