Please help me with the above parts to problem 2.121! I included the chater summ
ID: 3070935 • Letter: P
Question
Please help me with the above parts to problem 2.121! I included the chater summary as a reference. Also, please type answers or use computer if possible as handwriting has been hard to decipher. Thank you for the assistance!!
2.121 Eight is enough. A healthy body needs good food, ealthy 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: TEETH 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 data26 Age Rejected Yes No Under 20 20 to 25 25 to 30 30 to 35 35 to 40 Over 40 68 64711141783 2887 3801 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.Explanation / Answer
The study represented the following rejection data :
a.) The age of the applicants here is the explanatory variable and the choice of rejection ( Yes or No ) is the response because age is the governing factor behind the appropriate number of teeth that the candidate possesses.Based on the age,the criteria for proper teeth is studied, the appropiate choice of rejection is made and the response is noted.
b.) The joint distribution is found by dividing the count of each cell by the total number of observations which is 334321.
Hence the joint distribution is as below :
Expressing the joint densities as percentages by multiplying by 100, we get
Now it is clear to infer from the table that candidats aged between 20 and 25 have the least chances of rejection ie 23.32848% of them are not rejected.The chances of being rejected when aged above 40 is the most ie 1.136931% . Hence an important observation is that as age of the application increases, the chances of rejection increases.
c.) The marginal distributions are obtained as summing over the respective rows and columns.
The row totals indicate that of all applicants about 96.91913% of them are not rejected.
The column totals indicate that the most applicants are received in the age froup of 20-25 ie about 23.522%
d.) Since the choice of rejection is the response variable and age is the explanatory variable, we should should use the conditional distribution of response given a particular age group to explain the relationship between the two variables.
e.) The conditional distribution is obtained by fixing each column and dividing each cell in the column by the respective column total.
From this table, the conditional table thus obtained is :
Each cell in the conditional distribution table refers to the chances of being rejecteedor not rejected provided the candidate is from a specified age group.
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 58884 77992 55597 43994 47569 39985