Data:

Calories: 465, 634, 529, 316, 499, 589, 514, 307

Cholestrol: 41, 72, 68, 70, 75, 49 , 68, 41

a)For the data of Calories and Cholesterol given in the above table, can we conclude that Calories are useful predictor of Cholesterol? Use = 0.05.

b)Find 95% confidence interval of population regression coefficient of regression equation relating Calories and Cholesterol.

Q) A machine fills 12- ounce bottle with soda. In order for the machine to function properly, the standarddeviation of sample must be less than or equal to 0.03ounce.Sample of twelve bottles is selected, and the number of ounces of soda in each bottle is as follows.

12.03

12.10

12.02

11.98

13.50

11.0

12.00

12.05

11.97

11.91

12.90

12.95

a) At = 0.05, test the hypothesis that the machine is working properly?

Note: Please answer both questions within 60-70 minutes. Much appreciated.