Question

According to a national​ study, 38​% of taxpayers used computer software to do their taxes for a certain tax year. A sample of 135 taxpayers was selected. Complete parts a through d below.

a. Calculate the standard error of the proportion.

​(Round to four decimal places as​ needed.)

b. What is the probability that less than 35​% of the taxpayers from the sample used computer software to do their​ taxes?​P(Less than 35​% of the taxpayers sampled used computer

​(Round to four decimal places as​ needed.)

c. What is the probability that between 32​% and 43​% of the taxpayers from the sample used computer software to do their​ taxes?​

​(Round to four decimal places as​ needed.)

d. What impact would changing the sample size to 235 taxpayers have on the results of parts​ a, b, and​ c? Choose the correct answer below.

A. The standard error would be​ reduced, which​ would, in​ turn, reduce the probabilities that the sample proportions will be closer to the population proportion.

B. The standard error would be​ increased, which​ would, in​ turn, reduce the probabilities that the sample proportions will be closer to the population proportion.

C. The standard error would be​ reduced, which​ would, in​ turn, increase the probabilities that the sample proportions will be closer to the population proportion.

D. The standard error would be​ increased, which​ would, in​ turn, increase the probabilities that the sample proportions will be closer to the population proportion.

E. Changing the sample size would have no effect on the standard error or the probabilities that the sample proportions will be closer to the population proportion.

Answer 1

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Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(-0.7181, TRUE)" to find the probability.

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Refer Standard normal table/Z-table to find the probability or use excel formula "=NORM.S.DIST(1.1969, TRUE)" & "=NORM.S.DIST(-1.4363, TRUE)" to find the probability.

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The standard error would be reduced, which would, in turn, reduce the probabilities that sample proportions will be closer to the population proportion.