1. An airlines company is considering lowering the weight of check-in luggage allowed from the current 50 pounds. However, before making any changes, the airline wishes to estimate the average weight per bag checked by passengers. The airline randomly chooses 23 pieces of checked bags and finds an average weight of 38.5 pounds with a standard deviation of 3.79 pounds. a) Calculate the 95% confidence interval for the true population average weight per bag. Interpret your results (in terms of the problem). b) Suppose the airline decides to set the new limit at the lower confidence limit believing that now its new limit will often be exceeded and they could charge an overweight fee for extra revenue, comment on the validity of this belief (not an ethical issue or customer satisfaction issue). 2. A marketing company was concerned that in many homes, only cell phones were used. They were concerned that if they only called land-lines for their marketing research, they would not contact many of their customers. In order to further investigate the magnitude of the issue, the company mailed out a survey asking if the customer only used cell phones for phone service. The results of the survey showed 8% of the 250 respondents saying they only used cell phones. Calculate the 90% confidence interval for the true proportion that only used cell phones. Interpret your results (in terms of the problem). 3. A company was considering lowering its health care coverage for its employees. Part of the justification was the belief that the average amount of insurance claims filed by employees did not exceed $250. The company conducted a survey among 100 of its employees and calculated the test statistic to be 2.31. a) Is there sufficient evidence to refute the company's belief at the =.05 level of significance? State your conclusion in terms of the problem. b) What is the p-value of the test statistic