Pauly's Pizza claims that the mean time it takes for them to deliver a pizza to dorms at Nate's college is 30 minutes. After a long wait one night, Nate decides to test this claim. He randomly selects 15 dormitory residents and asks them to record the time it takes for Pauly's Pizza to deliver the next time they order pizza. Here are the results (in minutes). 31 38 39 25 26 45 42 32 23 38 42 21 40 37 28 (a) The sample mean is x = 33.8 and the sample standard deviation is sx = 7.72 . Calculate and interpret the standard error of the mean for these data. (b) Construct and interpret a 90% confidence interval for the true mean delivery time. Does the data support Pauly's claim