Question

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 distributed​ populations, 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
muμ	mu 1μ1	mu 2μ2
n	4040	4040
x overbarx	0.785420.78542 lb	0.805330.80533 lb
s	0.004450.00445 lb	0.007430.00743 lb

The test​ statistic, t, is

​(Round to two decimal places as​ needed.)

The​ P-value is

​(Round to three decimal places as​ needed.)

State the conclusion for the test.

A.

Fail to rejectFail to reject the null hypothesis. There is not is not

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.

Fail to reject Fail to 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.

C.

Reject the null hypothesis. There is not is not 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.

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

​(Round to three decimal places as​ needed.)

Does the confidence interval support the conclusion found with the hypothesis​ test?

Answer 1