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.
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.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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
- 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_____.(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 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. 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. 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.
D. 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 < u1 - u2 < ____ lb (Round to three decimal places as needed.)
- Does the confidence interval support the conclusion found with the hypothesis test?
▼ No,Yes, because the confidence interval contains ▼ Zero, Only negative values, Only positive values.
Transcribed Image Text:Regular
Data on the weights (Ib) 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
H2
26
n
26
X
0.79598 Ib
0.81941 Ib
0.00439 Ib
0.00745 Ib
S
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?
O A. Ho: H1= 2
H,: H1 # H2
O B. Ho: H1 = H2
H,: H1 < H2
O C. Ho: H1 = H2
H,: H1 > H2
O D. Ho: H1 #H2
H,: H1 <Hz
The test statistic, t, is- (Round to two decimal places as needed.)
The P-value is
(Round to three decimal places as needed.)
Transcribed Image Text:Regular
Data on the weights (Ib) 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
H2
26
26
0.79598 Ib
0.00439 Ib
n
0.81941 Ib
0.00745 Ib
O A. 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.
O 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.
O C. 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.
O D. 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).
| Ib<H, - H2<Ib
(Round to three decimal places as needed.)
Does the confidence interval support the conclusion found with the hypothesis test?
V because the confidence interval contains
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