Data on the weights(lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributedpopulations, and do not assume that the population standard deviations are equal. Complete parts(a) and(b) below. Use a 0.05 significance level for both parts.

Diet

Regular

1

2

n

20

20

x

0.78646 lb

0.80233 lb

s

0.00449 lb

0.00755 lb

a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda.

What are the null and alternativehypotheses?

A.

H0: 1=2

H1: 12

B.

H0: 1=2

H1: 1>2

C.

H0: 12

H1: 1<2

D.

H0: 1=2

H1: 1<2

The teststatistic, t, is

nothing

. (Round to two decimal places asneeded.)

TheP-value is

nothing

. (Round to three decimal places asneeded.)

State the conclusion for the test.

A.

Reject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

B.

Reject the null hypothesis. There isnot sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

C.

Failtoreject the null hypothesis. There isnot sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

D.

Failtoreject the null hypothesis. There is sufficient evidence to support the claim that the cans of diet soda have mean weights that are lower than the mean weight for the regular soda.

b. Construct a confidence interval appropriate for the hypothesis test in part(a).

nothing

lb<12<

nothing

lb

(Round to three decimal places asneeded.)

Does the confidence interval support the conclusion found with the hypothesistest?

No,

Yes,

because the confidence interval contains

only negative values.

only positive values.

zero.