Due: Sunday July 10 by 1 1:59pm on Gradescane Instructions: The purpose of this project is for you to apply the principles of estimation and hypothesis Ofsting. This is an individual project. Each person should turn in their own work. Show all of your work in linear fashion. You may type your work. List all calculator functions used. You must use an equation editor when necessary (Insert > Equation on most word processing software) Part 1 On March 4, 1999, the New England Journal of Medicine published a research article by Dr. Douglas locenby and colleagues comparing different treatments to help patients stop smoking. The four treatments were: a placebo, a nicotine patch, Zyban, and both Zyban and a nicotine patch. The subjects were treated and the number of subjects not smoking after 6 months was recorded. The results are summarized in the table below: Treatment Subjects participating Subjects not smoking After Six Months Placebo 160 30 Nicotine Patch 244 52 Zyban 244 85 Zyban and nicotine patch 245 95 1. Compute the sample proportion of successes for each group. Rank the four treatments in order of effectiveness (most effective to least effective). (5 pts.) 2. Calculate the 95% confidence interval for: a. The proportion of patients using Zyban who were not smoking 6 months later. Show all work. Round to 4 decimal places. (11 pts.) b. The proportion of patients using Zyban and a nicotine patch who were not smoking 6 months later. Show all work. Round to 4 decimal places. (11 pts.) 3. Using a scale appropriate for the two confidence intervals, draw the two confidence intervals on a number line. Label each so that they can be distinguished from each other. Use a ruler and mark even units. (8 pts.) 4. Based on the graph in #3, is there evidence that the Zyban plus patch is more effective than Zyban alone? Explain. (4 pts.) 5. The confidence intervals for the placebo and for the nicotine patch overlap, so we cannot conclude, based on them, whether the nicotine patch is more effective than the placebo. Carry out a hypothesis test to determine whether the success rate for the nicotine patch group is higher than the success rate for the placebo group. Use a level of significance of 0.05. Show all 6 steps in the process. What do the results suggest in terms of using a nicotine patch as treatment? Again, use complete sentences to explain your reasoning. (16 pts.) The margins of error in this study are fairly large. Suppose the researchers wanted to estimate the proportion of successes in each group, using 95% confidence, with a margin of error of 3%. What size samples would be required, using the study proportion for the placebo? (7 pts.)
