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 ofn₁=57people who are conservative voters showed thatr₁=44said yes. Another random sample ofn₂=63people who are liberal voters showed thatr₂=39said yes. Does this indicate that the population proportion of conservative voters who prefer art with fully clothed people is higher? Use= 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:p₁p₂
• H₀:p₁=p₂;H₁:p₁>p₂

(b)What sampling distribution will you use? What assumptions are you making?

• The Student'st. The number of trials is sufficiently large.
• The standard normal. We assume the population distributions are approximately normal.
• The Student'st. We assume the population distributions are approximately normal.
• The standard normal. The number of trials is sufficiently large.

(c) What is the value of the sample test statistic? (Test the differencep₁p₂. Do not use rounded values. Round your final answer to two decimal places.)

(d)Find (or estimate) theP-value. (Round your answer to four decimal places.)

(e) Sketch the sampling distribution and show the area corresponding to theP-value.

(f)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?

• At the= 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.
• At the= 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.
• At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
• At the= 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

(g)Interpret your conclusion in the context of the application.

• 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.
• 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 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.