H.2. In a Christmas tree survey 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 Natural X-tree Rural 160 64 Urban 261 89 a Give the null and alternative hypotheses that are appropriate for this problem. b. Test the null hypothesis. Give the test statistic and the P-value, and summarize the results. C. Give a 90% confidence interval for the difference in proportions. H.3. Coronary heart disease (CHD) begins in young adulthood and is the fifth leading cause of death among adults aged 20 to 24 years. However, studies of serum cholesterol levels among college students are scarce. One study at a southern university investigated the lipid levels in a cohort of sedentary university students. A total of 108 students volunteered for the study and met the eligibility criteria. The following table summarizes the blood lipid levels, in milligrams per deciliter (mg/dl), of the participants broken down by gender: Females (n = 71) Males (n = 37) Total cholesterol 173.70 34.79 171.81 33.24 LDL 96.38 29.78 109.44 31.05 HDL 61.62 13.75 46.47 7.94 a. Is it appropriate to use the two-sample t procedures to analyze these data for gender differences? Give reasons for your answer. b. Describe appropriate null and alternative hypotheses for comparing male and female total cholesterol levels. C. Carry out the significance test using a = 0.05. Report the test statistic with the degrees of freedom and the P-value. Write a short summary of your conclusion. d. Find a 95% confidence interval for the difference between the two means. Compare the information given by the interval with the information given by the significance test