Results of polls about belief in heaven and hell depend strongly on question wording. For instance, a survey conducted by the International Social Science Program at National Opinion Research Center (NORC) asked Americans whether they “definitely believe in heaven” or “definitely believe in hell” (see religioustolerance.org). The percentage who answered yes was 63.1% for heaven and 49.6% for hell.
a. Estimate the difference between the population proportions believing in heaven and believing in hell.
b. In this survey, suppose that 65 subjects believed in heaven but not in hell, whereas 35 believed in hell but not in heaven. Report the
(i) Assumptions.
(ii) Hypotheses,
(iii) Test statistic.
(iv) P-value, and
(v) Conclusion for testing that the probability of belief is the same for heaven and for hell.