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 μ μ1 mu 2μ2 n 4141 4141 (overbar)x 0.77984 lb 0.82336 lb s 0.00451 lb 0.00739 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?   The test​ statistic, t, is ______   The​ P-value is _______   State the conclusion for the test.   b. Construct a confidence interval appropriate for the hypothesis test in part​ (a). _____ lb < μ1 - μ2 <_____ lb Does the confidence interval support the conclusion found with the hypothesis​ test?

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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
μ
μ1
mu 2μ2
n
4141
4141
(overbar)x
0.77984 lb
0.82336 lb
s
0.00451 lb
0.00739 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?
 
The test​ statistic, t, is ______
 
The​ P-value is _______
 
State the conclusion for the test.
 
b. Construct a confidence interval appropriate for the hypothesis test in part​ (a).
_____ lb < μ1 - μ2 <_____ lb
Does the confidence interval support the conclusion found with the hypothesis​ test?
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