Question: Records in a three-county area show that in the last few years, Girl Scouts sell an average of 47.93 boxes of cookies per year, with a population standard deviation of 8.45 boxes per year. Fifty randomly selected Girl Scouts from the region sold an average of 46.54 boxes this year. Scout leaders are concerned that the demand for Girl Scout cookies may have decreased.
a. Test at the 10% significance level whether the average number of boxes of cookies sold by all Girl Scouts in the three-county area is lower than the historical average.
b. What will your decision be in part a if the probability of a Type I error is zero? Explain.