Chapter 10.4, Problem 64PB

Heaven and hell around the world Refer to the previous exercise. Results in this poll also depended strongly on the country in which the question was asked. For instance, the percentages believing in (heaven, hell) were (52%, 26%) in Ireland, (32%, 19%) in New Zealand, (28%, 22%) in Italy, (25%, 13%) in Great Britain, (21%, 11%) in the Netherlands, and (18%, 9%) in Germany. If for a given country you know the sample size was 1000, does this give you enough information to compare the two proportions inferentially for that country? Explain.

Heaven and hell 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 the National Opinion Research Center (NORC) asked Americans whether they “definitely believe in heaven” or “definitely believe in hell.” The percentage who answered yes was 63.1% for heaven and 49.6% for hell.

1. a. Estimate the difference between the population proportions believing in heaven and believing in hell.
2. 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.