An association of Christmas tree growers in Indiana sponsored a sample survey of 500 randomly selected Indiana houscholds 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. 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 n X(natural) 64 1 (rural) 160 2 (urban) 261 89 OConstruct 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. Do these data provide evidence of a significant difference in the proportion of rural and urban Indiana residents who had a natural Christmas tree this year? State hypotheses, then use your results from part (a) to help answer the question (no additional calculations are necessary).