2. (6 pts) In a survey of commuting habits, it was found that among 1068 homeowners. 824%% dive themselves to work. Among 1064 renters, 68. 1% drive themselves to work. Construct a 95%% combdence interval estimate of the difference between the proportion of homeowners who drive themselves to work and the proportion of renters who drive themselves to work. Base on the result, does there appear to be a significant difference between those two proportions? 3. A study was conducted to investigate the effectiveness of hypnotism in reducing pain Results for randomly selected subjects are given in the accompanying table. The values are before and affer hypnosis, the measurements are in centimeters on a pain scale. Use a 0.05 significance level to test the claim that the sensory measurements are lower after hypnotism. Assume the data come from a population have approximately normal. Subject A B C D E IF G Before 6.6 6.5 9.0 10.3 113 63 11.6 After 6.8 24 7.4 85 181 3.4 120 a. (2pts) Write the claim statement in sentence. b. (2 pts) State the null and alternate hypothesis in symbolic form C. (2 pts) Verify the requirements. d. (2 pts) Find P-value. Explain why you should or should not reject null hypothesis e. (2pts) Write the conclusion in sentence. 4. In a randomized double-blind placebo-controlled trial of children. Echinacea was tested as a treatment for upper respiratory infections in children. "Days of fever " was one criterion used to measure effects. Among 337 children treated with Echinacea, the mean number of days with fever was 0.81, with a standard deviation of 1 50 days. Among 370 children given a placebo, the mean number of days with fever was 0.64 with a standard deviation of 1.16 days. Use a 0.05 significance level to test the claim that Echinacea affects the number of days with fever. Base on the results, does Echinacea appear to be effective? ent in sentence qubolic form