11.45 (C2) en In a test of hypotheses about a difference in treatment pro- portions, what does it mean when the null hypothesis is not rejected? tre 11.47 Res effe The 11.46 (M4, M5, M6, P3) Many fundraisers ask for donations using e-mail and text messages. The paper "Now or Never! The Effect of Deadlines on Charitable Giving: Evidence from Two Natural Field Experiments" (Journal of Behavioral and Experimental Economics [2016]: 1-10) describes an experiment to inves- tigate whether the proportion of people who make a donation when asked for a donation by e-mail is different of Rar 10 ed In W from the proportion of people who make a donation when Ere asked for a donation in a text message. In this experi- ment, 1.32% of those who received and opened an e-mail request for a donation and 7.77% of those who received a text message asking for a donation actually made a dona- tion. Assume that the people who received these requests were randomly assigned to one of the two groups (e-mail or text message) and suppose that the given percentages are based on sample sizes of 2000 (the actual sample sizes in the experiment were much larger). a. The study described is an experiment with two treat- t ments. What are the two treatments? b. Is there convincing evidence that the proportion who make a donation is not the same for the two different methods? qCarry out a hypothesis test using a significance level of 0.05. nilnl od TECHNOLOGY NOTES ference Between Two Population Proportio c. Use a 90% confidence interval to estimate the differ- ence in the proportions who donate for the two different 0- treatments. 11.47 (M4, M5, M7, P4) c Researchers carried out an experiment to evaluate the effectiveness of using acupuncture to treat heel pain. The experiment is described in the paper "Effectiveness of Trigger Point Dry Needling for Plantar Heel Pain: A f Randomized Controlled Trial" (Physical Therapy [2014]: 1083-1094) and a follow-up response to a letter to the editor of the journal (Physical Therapy [2014]: 1354-1355) In this experiment, 84 patients experiencing heel pain were randomly assigned to one of two groups. received acupuncture and the other group received a sham treatment that consisted of using a blunt needle that did not penetrate the skin. Of the 43 patients in the sham treatment group, 17 reported pain reduction of more than 13 points on a foot pain scale (this was considered a meaningful reduction in pain). Of the 41 patients in the acupuncture group, 28 reported pain reduction of more than 13 points on the foot pain scale. nu)nod a. Use a 95% confidence interval to estimate the difference in the proportion who experience a meaningful pa reduction for the acupuncture treatment and for the sham One group treatment nooms d loodga b. What does the interval in Part (b) suggest about the effectiveness of acupuncture in reducing heel pain?