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 e
|
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 0.01 significance level for both parts. |
Diet |
Regular |
|||
|
μ |
μ1 |
μ2 |
|||
|
n |
24 |
24 |
|||
|
x |
0.79698 lb |
0.81096 lb |
|||
|
s |
0.00445 lb |
0.00748 lb |
- 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:
μ1=μ2
H1:
μ1<μ2
B.
H0:
μ1=μ2
H1:
μ1≠μ2
C.
H0:
μ1=μ2
H1:
μ1>μ2
D.
H0:
μ1≠μ2
H1:
μ1<μ2
The test statistic, t, is
nothing.
(Round to two decimal places as needed.)
The P-value is
nothing.
(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.
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.
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.
- Construct a confidence interval appropriate for the hypothesis test in part (a).
nothing
lb<μ1−μ2<nothing
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 positive values.
only negative values.
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