2. The aluminum bottle has become popular with beverage manufacturers. Besides being lightweight and requiring less packaging, the aluminum bottle is presorted to cool faster and stay cold longer than typical glass bottles. A small brewery tests this claim and obtains the following information regarding the time (in minutes) required to chill a bottle of beer from room temperatures (759F) to serving temperature (459F}. 50 clear glass bottles were tested with a mean time to chill of 126.2 minutes (5 = 9.9) and 44 aluminum bottles were tested with a mean time to chill of 92.4 minutes (5 = 7.3). (4.5 pts). a. What is the 80% condence interval for the mean difference in cooling time for clear glass versus aluminum? Use a t-critical of 1.302. (1.5 pts) b. What is the 95% condence interval for the mean difference in cooling time for clear glass versus aluminum? Use a t-critical of 2.017. (1.5 pts) c. Interpret your 95% confidence interval. Additionally, what does the 95% condence interval indicate about the differences in cooling time between the two bottles? (1.5 pts). 3. The following data represents the daily rental for a compact automobile charged by two car rental companies in 9 locations. You want to test whether Thrifty has a significantly different cost than Hertz, on average. Large cities were randomly sampled for the study and you may assume that car rental prices are normally distributed in the population. Conduct the appropriate test to determine if there are differences in price, on average, for cities between the two companies. Use a t-critical of 2.306(6 pts) City Chicago Los Angeles Houston Orlando Boston Seattle Pittsburgh Phoenix New Orleans Average Stdev 9.32 9.40 a. What are the null and the alternative hypotheses? (1 pts) b. What are the assumptions (conditions) of this test, and were they met? Why or why not? (.5 pts) c. Perform the appropriate test including the formula that you used, the calculated value of the t-statistic (show all workl), and the t-critical you compared to your t- statistic. (2.5 pts) d. State your conclusion. (2 pts)