1. the heights were recorded for a simple random sample of 270 junior. the mean of this sample was 66.5 inches. the heights are known to be normally distributed with a population standard deviation of 5.1 inches. at a 0.05 significance level, test the claim that the average height of a freshman differs from the 1956 average freshman height of 65.8 inches. i. state the null and alternative hypotheses. ii. state the significance level for this problem.