1. Complete the following using the BodyFat data file. Some questions require you to set up and calculate the answers yourselves and use Stata to verify. Be sure and use the slides/book/or other...

1.
Complete the following using the BodyFat data file. Some questions require you to set up and calculate the answers yourselves and use Stata to verify. Be sure and use the slides/book/or other resources to help you express formulas appropriately and correctly.

1. Use Stata to create a new categorical variable called age_cat that dichotomizes age on the median age value. (You will need to determine this value based on the distribution of age). Use Stata to generate these thresholds, displaying the Stata results. Assign appropriate labels to variable and categories.

2. Construct box plots and summary statistics of bodyfat by the age categories variable you created in a. Comment and provide interpretation of the distributions of body fat among the age groups.


3. What test can be used to assess whether the mean bodyfat differs among young versus older men?

4. Implement the test in c and report a two-tailed p-value. Conduct the test by hand using appropriate expressions of relevant formulas, and verify using Stata. Note you will need to provide appropriate justification for the test you use and justify assumptions analytically. Assume a Type I error rate of 0.05. Interpret your results and conclusions of the test.


5. Compute the 95% CI associated with the hypothesis and interpret based on hypothesis test.

Sheet: Bodyfat (1) Density bodyfat Age Weight Height Neck Chest Abdomen Hip Thigh Knee Ankle Biceps Forearm Wrist 1.0708 36.2 37.3 17.1 1.0853 37.3 1.0414 16.6 1.0751 37.3 1.034 32.2 1.0502 35.7 1.0549 38.3 1.0704 37.8 1.09 4.1 38.3 1.0722 1.083 39.7 25.2 32.8 1.0812 39.2 25.9 37.2 1.0513 38.3 1.0505 1.0484 1.0512 38.7 16.9 1.0333 40.8 23.1 36.2 1.0468 66.9 38.2 1.0622 38.7 22.9 37.2 1.061 1.0551 19.1 18.4 1.064 32.8 19.9 1.0631 76.4 35.3 1.0584 36.2 17.1 1.0668 17.6 1.0911 35.7 36.7 1.0811 36.2 88.6 74.6 34.7 1.0468 38.8 1.091 73.9 1.079 8.8 36.7 35.3 17.6 1.0716 38.7 38.7 18.4 1.0862 37.3 38.8 17.9 1.0719 79.1 36.2 1.0502 39.8 67.1 1.0263 32.3 37.3 1.0101 38.3 1.0438 1.0346 33.2 30.5 19.4 1.0202 35.2 136.2 148.1 147.7 1.0258 40.2 1.0217 128.3 32.7 21.4 1.025 70.6 17.4 1.0279 37.3 36.7 29.8 18.4 1.0269 40.2 23.0 35.8 1.0814 34.7 16.1 1.067 35.7 38.2 1.0742 1.0665 17.9 1.0678 32.8 35.8 1.0903 70.4 1.0756 10.2 37.2 1.084 34.3 89.2 77.9 1.0807 33.7 16.9 1.0848 79.6 1.0906 37.8 87.6 77.6 1.0473 18.9 1.0524 20.4 1.0356 39.8 22.7 37.7 1.028 1.043 37.7 1.0396 36.2 1.0317 1.0298 32.7 29.9 19.1 1.0403 1.0264 32.3 35.3 31.1 18.4 1.0313 40.2 22.7 34.8 1.0499 17.4 1.0673 32.8 1.0847 78.4 18.1 1.0693 36.3 1.0439 18.6 1.0788 8.8 38.7 1.0796 1.068 33.2 19.1 16.9 1.072 35.2 1.0666 1.079 8.8 38.7 39.7 18.1 1.0483 38.7 38.3 1.0498 37.8 1.056 39.3 1.0283 38.2 1.0382 1.0568 18.4 39.3 34.3 1.0377 38.7 1.0378 1.0386 37.8 33.7 1.0648 37.7 37.7 1.0462 18.1 1.08 8.3 1.0666 36.7 1.052 37.2 38.2 1.0573 39.2 39.7 1.0795 38.3 18.4 1.0424 33.3 29.6 19.1 1.0785 37.3 1.0991 17.4 20.4 1.077 1.073 38.7 39.3 1.0582 37.3 1.0484 35.3 1.0506 32.2 31.0 18.6 1.0524 20.4 1.053 20.1 36.3 18.4 1.048 40.7 39.8 1.0412 1.0578 1.0547 39.3 18.1 1.0569 38.7 19.1 1.0593 34.2 36.8 1.0538 37.2 33.3 28.2 18.1 1.0355 17.4 1.0486 40.2 35.3 1.0503 35.3 37.8 17.4 1.0384 1.0607 36.3 36.3 1.0529 20.1 36.8 18.1 1.0671 38.8 1.0404 38.3 64.6 1.0575 18.1 39.2 1.0358 40.8 39.3 1.0414 18.4 1.0652 38.7 17.6 1.0623 17.6 1.0674 37.7 1.0587 17.6 1.0373 36.8 22.2 33.8 1.059 17.4 35.8 17.4 1.0515 39.8 33.3 29.6 18.1 1.0648 38.3 1.0575 18.1 38.7 17.6 1.0472 36.3 17.1 1.0452 37.8 17.9 1.0398 37.8 1.0435 18.1 1.0374 37.8 17.6 1.0491 32.7 28.3 17.1 37.7 39.2 23.8 34.3 1.0481 34.3 17.6 1.0522 20.4 40.8 1.0422 16.6 1.0571 38.2 1.0459 36.7 17.9 1.0775 77.1 1.0754 1.0664 35.7 92.7 81.9 39.2 1.0322 68.4 40.8 24.6 33.3 29.7 18.4 1.0873 35.2 35.7 16.9 1.0416 67.6 18.4 1.0776 77.6 20.4 1.0542 19.6 72.9 33.8 19.6 1.0758 36.8 17.4 1.061 17.9 1.051 38.2 33.7 29.2 19.4 1.0594 37.8 21.7 32.2 1.0287 68.6 35.2 30.7 19.1 1.0761 18.6 1.0704 76.6 34.8 16.9 1.0477 36.2 1.0775 1.0653 19.1 1.069 40.7 37.3 1.0644 20.4 1.037 1.0549 33.7 19.4 1.0492 34.2 37.2 1.018 34.3 74.4 1.061 17.4 1.0926 81.9 36.2 1.0983 34.8 16.9 1.0521 37.3 1.0603 16.9 38.7 37.7 1.0414 20.1 1.0763 79.4 34.8 16.9 1.0689 35.3 1.0316 18.4 1.0477 34.8 30.3 18.1 1.0603 16.9 19.9 1.0387 68.1 1.1089 33.8 79.3 69.4 36.2 1.0713 35.3 17.4 1.0587 37.7 1.0794 39.7 1.0453 37.2 1.0524 20.4 39.8 19.1 1.052 40.8 1.0434 1.0728 80.6 36.3 17.9 1.014 19.9 1.0624 40.7 1.0429 33.7 1.047 17.1 1.0411 1.0488 17.4 1.0583 16.9 1.0841 1.0462 33.8 1.0709 37.8 39.2 18.6 1.0484 35.2 35.7 17.4 1.034 38.3 1.0854 18.4 1.0209 34.8 40.3 21.8 34.8 30.7 17.4 1.061 16.6 39.8 24.1 37.3 23.1 19.4 1.025 1.0254 32.8 40.2 36.7 31.6 18.4 1.0771 36.2 1.0742 38.2 17.6 1.0829 35.8 91.2 79.4 17.4 1.0373 40.2 40.3 23.2 36.8 31.0 18.9 1.0543 38.3 38.8 18.6 1.0561 32.7 1.0543 34.7 29.1 18.4 1.0678 34.8 92.8 81.1 1.0819 18.6 1.0433 39.2 22.9 35.7 1.0646 36.2 17.1 1.0706 18.9 1.0399 19.6 1.0726 40.2 1.0874 35.2 35.2 1.074 1.0703 37.2 1.0418 38.3 33.2 30.0 18.4 1.0647 1.0601 38.8 1.0745 35.2 16.9 1.062 16.1 1.0636 1.0384 17.6 1.0403 35.7 1.0563 18.6 38.3 1.0424 40.3 1.0372 40.2 1.0705 1.0316 40.8 19.1 1.0599 34.7 20.1 1.0207 38.8 19.4 1.0304 1.0256 65.6 35.3 1.0334 40.7 38.8 1.0641 36.3 1.0308 40.8 1.0736 34.8 1.0236 40.8 23.2 35.2 28.6 20.1 1.0328 37.3 1.0399 1.0271 40.8 33.7