Question

In an analysis investigating the usefulness of pennies, the cents portions of 113 randomly selected credit card charges from students are recorded, and they have a mean of 47.6 cents and a standard deviation of 32.3 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. a. Identify the null and alternative hypotheses. Choose the correct answer below. O A. Hp: 28.866 cents O c. Ho: ơ : 28.866 cents O B. Ho: 02 28.866 cents H1 . ơe28. 866 cents OD. Ho: σ#28.866 cents Η, σ. 28 866 cents H1 : σ t 28 866 cents H.σ:28 866 cents b. Compute the test statistic (Round to three decimal places as needed.) c. Find the P-value of the test statistic. The P-value of the test statistic is Round to three decimal places as needed.) d. State the conclusion ' Ho There ▼ sufficient evidence to warrant rejection of the claim hat the cents port on of credit card transactions has a standard deviation equal to 28 866 cents e. If the amounts from 0 cents to 99 cents are all equally likely, is the requirement of a normal distribution satisfied? If not, how does that affect the conclusion? O 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 O B. Yes, because in that case the underlying population is normally distributed, so the results of standard deviation hypothesis tests are reliable O C. No, because in that case the underlying population is not normally distributed, so the results of standard deviation hypothesis tests are not reliable 。D. Yes, because in that case he sampling distribution o standard deviations is approximately no a distributed so he results of standar de ation v tesis ests are e able.

Answer 1

a)

option A is correct

b)

X² =(n-1)(s/ $\sigma$ )² =(113-1)*(32.3/28.866)² =140.233

c) p value =0.073

d)

fail to reject Ho ; there is not sufficient evidence,,,,,,,

e)

option B