Do you prefer paintings in which the people are fully clothed? This question was asked by a professional survey group on behalf of the National Arts Society. A random sample of n1 = 59 people who are conservative voters showed that r1 = 45 said yes. Another random sample of n2 = 62 people who are liberal voters showed that r2 = 36 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.
Please provide the following information:
(a) What is the level of significance? State the null and alternate hypotheses.
(b) What sampling distribution will you use? What assumptions are you making? Compute the sample test statistic.
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a)–(c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
(e) Interpret your conclusion in the context of the application.