Lance, a long time proprietor of a men's clothing store in Peru, Illinois, has noticed that in the past few years that he has a lot more shorter pants than longer pants that he is trying to get rid of. Lance suspects that this is a result of men are now taller on average than they once were. Lance had been relying on the same statistical charts that he had when he opened the store 30 years ago that stated that the average height of an adult male was 5.76 feet (a little more than 5 feet 8 inches tall). For years Lance had used that information, assumed a normal distribution and applied his knowledge from statistic class to determine his orders. This approach had been successful for many years, until recently. Lance decided to conduct a survey to determine whether there was evidence that adult males had, on average, grown taller than 5.76 feet. So he randomly sampled 75 male customers and found their average height was 5.9 feet with a standard deviation of .48 feet.
Is their sufficient evidence at a .01 level of significance that the average male height now exceeds 5.76 feet?
Using Lance's sample, construct a 95% confidence interval for the current population mean.