Question

A) Would you favor spending more federal tax money on the arts? Of a random sample of n₁ = 92 politically conservative voters, r₁ = 19 responded yes. Another random sample of n₂ = 85 politically moderate voters showed that r₂ = 21 responded yes. Does this information indicate that the population proportion of conservative voters inclined to spend more federal tax money on funding the arts is less than the proportion of moderate voters so inclined? Use α = 0.05.

What is the value of the sample test statistic? (Test the difference p₁ − p₂. Do not use rounded values. Round your final answer to two decimal places.)

Find (or estimate) the P-value. (Round your answer to four decimal places.)

B) Would you favor spending more federal tax money on the arts? Of a random sample of n₁ = 233 women, r₁ = 63 responded yes. Another random sample of n₂ = 161 men showed that r₂ = 48 responded yes. Does this information indicate a difference (either way) between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts? Use α = 0.05.

What is the value of the sample test statistic? (Test the difference p₁ − p₂. Do not use rounded values. Round your final answer to two decimal places.)

Find (or estimate) the P-value. (Round your answer to four decimal places.)

Answer 1

Answer(A):

Sample size of politically conservative voters, n1=92

Number of politically conservative voters who responded yes, r1 = 19

Sample size of politically moderate voters, n2=85

Number of politically moderate voters who responded yes, r2 = 21

The proportion of politically conservative voters who responded yes= p1= 19/92

                                                                                   p1= 0.2

The proportion of politically moderate voters who responded yes = p2= 21/85

                                                                                   p2= 0.2470588

We have to test

H0: P1=P2

HA: P1< P2

The test statistic to test this hypothesis is z test for two proportions.

The test statistic is given by

Where p=40/177= 0.2259887

The p-value for the above test is 0.2273

The above p-value is 0.2273 is greater than 0.05 which indicates that we do not have enough evidence against the null hypothesis to reject it, so we fail to reject the null hypothesis and we cannot conclude that the population proportion of conservative voters inclined to spend more federal tax money on funding the arts is less than the proportion of moderate voters so inclined.

Answer(B):

Sample size of women respondents, n1=233

Number of women who responded yes, r1 = 63

Sample size of men respondents, n2=161

Number of men who responded yes, r2 = 48

The proportion of women who responded yes= p1= 63/233

                                                                                   p1= 0.2703863

The proportion of men who responded yes = p2= 48/161

                                                                                   p2= 0.2981366

We have to test

H0: P1=P2

HA: P1≠ P2

The test statistic to test this hypothesis is z test for two proportions.

The test statistic is given by

Where p=111/ 394= 0.2817259

The p-value for the above test is 0.5472

The above p-value is 0.5472 is greater than 0.05 which indicates that we do not have enough evidence against the null hypothesis to reject it, so we fail to reject the null hypothesis and we cannot conclude that there is a difference between the population proportion of women and the population proportion of men who favor spending more federal tax dollars on the arts.