In an analysis investigating the usefulness of pennies, the cents portions of 104 randomly selected credit card charges from students are recorded, and they have a mean of 47.6 cents and a standard deviation of 30.4 cents. If the amounts from 0 cents to 99 cents are all equally likely, the mean is expected to be 49.5 cents and the population standard deviation is expected to be 28.866 cents. Use a 0.025 significance level to test the claim that the sample is from a population with a standard deviation equal to 28.866 cents. Complete parts (a) through (e) below. Question content area bottom Part 1 a. Identify the null and alternative hypotheses. Choose the correct answer below. A. H0: σ≥28.866 cents H1: σ<28.866 cents B. H0: σ=28.866 cents H1: σ≠28.866 cents C. H0: σ=28.866 cents H1: σ>28.866 cents D. H0: σ≠28.866 cents H1: σ=28.866 cents Part 2 b. Compute the test statistic. χ2=enter your response here (Round to three decimal places as needed.) Part 3 c. Find the P-value of the test statistic. The P-value of the test statistic is enter your response here. (Round to three decimal places as needed.)
In an analysis investigating the usefulness of pennies, the cents portions of 104 randomly selected credit card charges from students are recorded, and they have a mean of 47.6 cents and a standard deviation of 30.4 cents. If the amounts from 0 cents to 99 cents are all equally likely, the mean is expected to be 49.5 cents and the population standard deviation is expected to be 28.866 cents. Use a 0.025 significance level to test the claim that the sample is from a population with a standard deviation equal to 28.866 cents. Complete parts (a) through (e) below.
Question content area bottom
Part 1
a. Identify the null and alternative hypotheses. Choose the correct answer below.
A.
H0: σ≥28.866 cents
H1: σ<28.866 cents
B.
H0: σ=28.866 cents
H1: σ≠28.866 cents
C.
H0: σ=28.866 cents
H1: σ>28.866 cents
D.
H0: σ≠28.866 cents
H1: σ=28.866 cents
Part 2
b. Compute the test statistic.
χ2=enter your response here
(Round to three decimal places as needed.)
Part 3
c. Find the P-value of the test statistic.
The P-value of the test statistic is enter your response here.
(Round to three decimal places as needed.)
Part 4
d. State the conclusion.
Do not reject
Do not reject
Reject
H0. There
is not
is
is not
sufficient evidence to warrant rejection of the claim that the cents portion of credit card transactions has a standard deviation equal to 28.866 cents.
Part 5
e. If the amounts from 0 cents to 99 cents are all equally likely, is the requirement of a
A.
No, because in that case the underlying population is not normally distributed, but the central limit theorem indicates that the conclusion is still valid.
B.
No, because in that case the underlying population is not normally distributed, so the results of standard deviation hypothesis tests are not reliable.
C.
Yes, because in that case the underlying population is normally distributed, so the results of standard deviation hypothesis tests are reliable.
D.
Yes, because in that case the sampling distribution of standard deviations is approximately normally distributed, so the results of standard deviation hypothesis tests are reliable .
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