2.121 Eight is enough. A healthy body needs good food, and healthy teeth are needed to chew our food so that it can nourish our bodies. The U.S. Army has recognized this fact and requires recruits to pass a dental examination. If you wanted to be a soldier in the Spanish American War, which took place in 1898, you needed to have at least eight teeth. Here is the statement of the requirement:
Unless an applicant has at least four sound double teeth, one above and one below on each side of the mouth, and so opposed as to serve the purpose of mastication, he should be rejected.
A study reported the rejection data for enlistment candidates classified by age. Here are the data:26
| Age | ||||||
|---|---|---|---|---|---|---|
| Rejected | Under 20 | 20 to 25 | 25 to 30 | 30 to 35 | 35 to 40 | Over 40 |
| Yes | 68 | 647 | 1114 | 1783 | 2887 | 3801 |
| No | 58,884 | 77,992 | 55,597 | 43,994 | 47,569 | 39,985 |
(a) Which variable is the explanatory variable? Which variable is the response variable? Give reasons for your answer.
(b) Find the joint distribution. Write a brief summary explaining the major features of this distribution.
(c) Find the two marginal distributions. Write a brief summary explaining the major features of these distributions.
(d) Which conditional distribution would you choose to explain the relationship between these two variables? Explain your answer.
(e) Find the conditional distribution that you chose in part (d), and write a summary that includes your interpretation of the relationship based on this conditional distribution.