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 ð‘› = 400 and ð‘¥Ì… = 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.
3. Several measurements were made on 54 anesthetized wild bears. The file “bears.csv” on Canvas contains the distance around the neck (in inches) and weight (in pounds) of each bear.
Suppose we want to estimate the mean weight of all wild bears. Use StatKey to create a bootstrap distribution (consisting of at least 5000 bootstrap samples) based on the weights of the bears in the sample. Just like in the second problem, uploading a file will be preferable to retyping the sample data. You will have to select a variable when you upload “bears.csv” – since you want to estimate the mean weight, select the weight column. Regardless of whether you upload the csv file or retype the sample data into StatKey, your original sample should have ð‘› = 54 and ð‘¥Ì… = 182.889.
After constructing the bootstrap distribution, determine a 99% confidence interval for the mean weight of all wild bears. Then copy screenshots of the bootstrap dot plot (with percentiles visible) and original sample box into your assignment.
Note: On this assignment, none of the problems have partial credit. Since each problem is worth 4 points, there are four items that will be checked, which are listed below. If all four items are correct, the grade on that problem will be 4/4. If at least one item is incorrect, the grade on that problem will be 0/4. The four items are as follows:
confidence interval
Also, since this assignment is supposed to emulate part of the group project, your StatKey screen shots should be cropped, and the assignment should be submitted as one file, not three. As far as cropping the screen shots is concerned, you don’t have to crop very much out – the easiest thing to do is crop everything outside of a rectangle containing the bootstrap distribution, original sample, and bootstrap sample (even though you don’t really need the individual bootstrap sample in the lower right). The cropped screen shots in the “Proportion Example” file were cropped that way.
The easiest way to submit the assignment is to copy your cropped screen shots into a blank word processing document (like a blank Microsoft Word file), and then save that document as a pdf.
If your screen shots are not cropped and/or your assignment is not submitted as one file, one point will be subtracted from your grade on the assignment.
