Based on information from Harper’s Index, r1 = 37 out of a random sample of n1 = 100 adult Americans who did not attend college believe in extraterrestrials. However, out of a random sample of n2 = 100 adult Americans who did attend college, r2 = 47 claim that they believe in extraterrestrials. Does this indicate that the proportion of people who attended college and who believe in extraterrestrials is higher than the proportion who did not attend college? Use α = 0.01.
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.