Question

1. An association of Christmas tree growers in Indiana sponsored a sample survey of Indiana households to help improve the marketing of Christmas trees. 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 410 households displaying a Christmas tree 160 lived rural area and 250 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 is the data:

Population	n	Natural (X)
Rural (1)	160	62
Urban (2)	20	86

a) 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. b) Test the null hypothesis. Give the test statistic and the p-value, and your conclusion. c) Give a 90% confidence interval for the difference in proportions

Answer 1

Population	n	Natural (X)	p^=X/n
Rural (1)	160	62	0.3875
Urban (2)	250	86	0.344