Question 8.69

8.69 Natural versus artificial Christmas trees.

CASE 8.2 In the Christmas tree survey introduced in Case 8.2 (page 428), respondents who had a tree during the holiday season were asked whether the tree was natural or artificial. Respondents were also asked if they lived in an urban area or in a rural area. Of the 421 households displaying a Christmas tree, 160 lived in rural areas and 261 were urban residents. The tree growers want to know if there is a difference in preference for natural trees versus artificial trees between urban and rural households. Here are the data:

Population (natural)
1 (rural) 160 64
2 (urban) 261 89
  1. Give the null and alternative hypotheses that are appropriate for this problem, assuming we have no prior information suggesting that one population would have a higher preference than the other.
  2. Test the null hypothesis. Give the test statistic and the -value, and summarize the results.
  3. Give a 90% confidence interval for the difference in proportions.

8.69

(a) . (b) . The data do not show a difference in preference for natural trees versus artificial trees between urban and rural households. (c) (−0.021, 0.139).