1.A tire manufacturer is interested in testing the fuel economy for two different tread patterns.Tires of each tread type were driven for 2000 miles on each of 10 different cars.The mileages, in miles per gallon were as follows:

Car TREAD A TREAD B

A 24.7 20.3

B 22.5 19.0

C 24.0 22.5

D 26.9 23.1

E 22.4 20.6

F 26.5 23.6

G 27.2 24.1.6

H 19.7 19.5

I 27.5 22.9

J 23.4 24.3

A.Construct a 92% confidence interval for the mean difference in fuel economy.

B.Based on the confidence interval, is it reasonable to believe that the mean mileage may be the same for both types of tread?

C.Conduct a hypothesis test for the mean difference in fuel economy.State the null and alternate hypothesis, the test statistic and the p-value.At the 4% significance level, does this test provide good evidence that the mean mileage of the cars is different based on the tread pattern of their tires?State the decision.

2.Are low fat diets or low carb diets more effective for weight loss?A sample of 75 subjects went on a low carb diet for six months.At the end of that time , the sample mean weight loss was 4.7 kg with a sample standard deviation of 7.16 kg.A second sample of 82 subjects went on a low fat diet. Their sample mean wight loss was 2.1 kg with a standard deviation of 3.3 kg.Can you conclude that the mean weight loss is different between the two diets?

A.Construct a 90% confidence interval for the mean difference in weight loss.

B.Based on the confidence interval, is it reasonable to believe that the mean weight loss is different for both diets?

C.Conduct a hypothesis test.State the null and alternate hypothesis, the test statistic and the p-value.State the decision based on the 5% significance level.