Question

Do you prefer paintings in which the people are fully clothed? This question was asked by a professional survey group on behalf of a national arts organization. A random sample of n1 = 56 people who are conservative voters showed that r1 = 43 said yes. Another random sample of n2 = 65 people who are liberal voters showed that r2 = 37 said yes. Does this indicate that the population proportion of conservative voters who prefer art with fully clothed people is higher? Use α = 0.05. (a) What is the level of significance? State the null and alternate hypotheses. H0: p1 = p2; H1: p1 < p2 H0: p1 = p2; H1: p1 ≠ p2 H0: p1 = p2; H1: p1 > p2 H0: p1 > p2; H1: p1 = p2 (b) What sampling distribution will you use? What assumptions are you making? The standard normal. We assume the population distributions are approximately normal. The standard normal. The number of trials is sufficiently large. The Student's t. We assume the population distributions are approximately normal. The Student's t. The number of trials is sufficiently large. 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.) (c) Find (or estimate) the P-value. (Round your answer to four decimal places.) Sketch the sampling distribution and show the area corresponding to the P-value. Maple Generated Plot Maple Generated Plot Maple Generated Plot Maple Generated Plot (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. (e) Interpret your conclusion in the context of the application. Fail to reject the null hypothesis, there is sufficient evidence that the proportion of conservative voters who prefer art with fully clothed people is higher. Reject the null hypothesis, there is insufficient evidence that the proportion of conservative voters who prefer art with fully clothed people is higher. Reject the null hypothesis, there is sufficient evidence that the proportion of conservative voters who prefer art with fully clothed people is higher. Fail to reject the null hypothesis, there is insufficient evidence that the proportion of conservative voters who prefer art with fully clothed people is higher.

Answer 1