STA 296: Statistical Methods and Motivations Other Graded Assignments #4 – Due Friday, February 16 Submission: Upload and submit your completed assignment on Canvas before 11:59 PM on February 16, 2018. Make sure the document you upload has file extension .pdf. 1. In order to estimate the proportion of all dentists who recommend a specific brand of toothpaste, a consumer protection group randomly samples 400 dentists, and finds that 330 recommend that brand. Suppose we want to estimate the proportion of all dentists who recommend that brand of toothpaste. Use StatKey to construct a bootstrap distribution (consisting of at least 5000 bootstrap samples), and then use percentiles to find a 90% confidence interval for the

relevant population proportion. Copy screenshots of the

bootstrap dot plot (with percentiles visible) and

original sample box into your assignment. 2. Now, construct the same interval as in the first problem, but use the “CI for Single Mean” option on StatKey instead of “CI for Single Proportion”. To estimate a proportion as though you are estimating a mean, each individual needs to be listed numerically as either a 1 (for a success) or a 0 (for a failure). In this context, a success occurs when a dentist recommends the toothpaste, and a failure occurs when a dentist does not recommend the toothpaste. Consequently, your sample will consist of 330 ones and 70 zeros. The file “toothpaste.csv” on Canvas contains the

sample data expressed as ones and zeros. If you would rather not type out 330 ones and 70 zeros manually, select “Upload File” in StatKey (instead of “Edit Data”), and upload toothpaste.csv. (Note: You will have to save the csv file first before you can upload it. You cannot upload it from Canvas.) You will be prompted to select a column. At this point, select the only available column (click on the word “recommendation”, then “OK”), and the sample data will upload to StatKey. Whether you use the csv file or enter the data manually, the original sample should have ?? = 400 and ??¯= 0.825. Just like in the first problem, construct a bootstrap distribution (consisting of at least 5000 bootstrap samples), and use percentiles to find a 90% confidence interval for the proportion of all dentists who recommend that brand of toothpaste. Then copy screenshots of the bootstrap dot plot (with percentiles visible) and original sample box into your assignment. The

confidence interval endpoints that you get in this problem should be very close (if not identical) to the ones you got in the first problem.