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 ? ?1 ?2 n 28 28 x? 0.79191 lb 0.81624 lb s 0.00442 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 alternative hypotheses? A. H0: ?1 = ?2 H1: ?1 < ?2 B. H0: ?1 = ?2 H1: ?1 > ?2 C. H0: ?1 ? ?2 H1: ?1 < ?2 D. H0: ?1 = ?2 H1: ?1 ? ?2 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 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 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 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. Fail to reject the null hypothesis. There 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. Construct a confidence interval appropriate for the hypothesis test in part (a). lb < ?1 - ?2 < lb (Round to three decimal places as needed.) Does the confidence interval support the conclusion found with the hypothesis test? Yes, because the confidence interval contains only negative values. only positive values. zero.

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
? ?1 ?2
n 28 28
x? 0.79191 lb 0.81624 lb
s 0.00442 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 alternative hypotheses?

A. H0: ?1 = ?2
H1: ?1 < ?2
B. H0: ?1 = ?2
H1: ?1 > ?2
C. H0: ?1 ? ?2
H1: ?1 < ?2
D. H0: ?1 = ?2
H1: ?1 ? ?2

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 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 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 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. Fail to reject the null hypothesis. There 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. Construct a confidence interval appropriate for the hypothesis test in part (a).
lb < ?1 - ?2 < lb
(Round to three decimal places as needed.)

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

Yes, because the confidence interval contains
only negative values.
only positive values.
zero.

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
? ?1 ?2
n 28 28
x? 0.79191 lb 0.81624 lb
s 0.00442 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 alternative hypotheses?

A. H0: ?1 = ?2
H1: ?1 < ?2
B. H0: ?1 = ?2
H1: ?1 > ?2
C. H0: ?1 ? ?2
H1: ?1 < ?2
D. H0: ?1 = ?2
H1: ?1 ? ?2

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 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 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 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. Fail to reject the null hypothesis. There 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. Construct a confidence interval appropriate for the hypothesis test in part (a).
lb < ?1 - ?2 < lb
(Round to three decimal places as needed.)

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

Yes, because the confidence interval contains
only negative values.
only positive values.
zero.

Added by Dawn L.

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