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 (75ef) to serving temperature (459f). 45 clear glass bottles were tested with a mean time to chill of 133.8 minutes (s = 9.9) and 35 aluminum bottles were tested with a mean time to chill of 92.4 minutes (s 7.3).

a. what is the 80% confidence interval for the mean difference in cooling time for clear glass versus aluminum?
b. what is the 95% confidence interval for the mean difference in cooling time for clear glass versus aluminum?
c. what does the 95% confidence interval indicate about the difference in cooling time between the two bottles?