An association of Christmas tree growers in Indiana sponsored a sample survey of 500 randomly selected Indiana households to help improve the marketing of Christmas trees. One question the researchers asked was, "Did you have a Christmas tree this year?" 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. The tree growers want to know if there is a difference in preference for natural trees versus artificial trees between urban and rural households. Among the 160 who lived in rural areas, 64 had a natural tree. Among the 261 who lived in an urban area, 89 had a natural tree.

(a) Construct and interpret a 95% confidence interval for the difference in the proportion of rural and urban Indiana residents who had a natural Christmas tree this year.

(b)) Suppose the tree growers asked 10 different questions about Christmas tree preferences in an effort to find differences between urban and rural residents. Explain why it would be unwise to perform 10 different 2-sample significance tests ( = 0.05) on their data and conclude that any significant result establishes a difference between the two groups.