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Applying Statistics on Health Metrics

A) Treating breast cancer. The most common treatment for breast cancer was once removal of the breast. It is now usual to remove only the tumor and nearby lymph nodes, followed by radiation. The change in policy was due to a large medical experiment that compared the two treatments. Each treatment was given to a separate group of breast cancer patients, chosen at random. The patients were closely followed to see how long they lived following surgery. What are the explanatory and response variables? Are they categorical or quantitative variables?

b) Do heavier people burn more energy? Metabolic rate, the rate at which the body consumes energy, is important in studies of weight gain, dieting, and exercise. Here are data on the lean body mass and resting metabolic rate for 12 women and 7 men who are subjects in a study of dieting. Lean body mass, given in kilograms, is a person's weight leaving out all fat. Metabolic rate is measured in calories burned per 24 hours, the same calories used to describe the energy content of foods. The researchers believe that lean body mass is an important influence on metabolic rate.

Subject Sex Mass (kg) Rate (cal) Subject Sex Mass (kg) Rate (cal)
1 M 62.0 1792 11 F 40.3 1189
2 M 62.9 1666 12 F 33.1 913
3 F 36.1 995 13 M 51.9 1460
4 F 54.6 1425 14 F 42.4 1124
5 F 48.5 1396 15 F 34.5 1052
6 F 42.0 1418 16 F 51.1 1347
7 M 47.4 1362 17 F 41.2 1204
8 F 50.6 1502 18 M 51.9 1867
9 F 42.0 1256 19 M 46.9 1439
10 M 48.7 1614

(1) Place the above data on an Excel spreadsheet and use the chart wizard to construct a scatter plot of the data for the female subjects. Which is the explanatory variable?
(2) Is the association between these variables positive or negative? What is the form of the relationship? How strong is the relationship?
(3) Now add the data for the male subjects to your graph, using a different color or
a different plotting symbol. Does the pattern of relationship that you observed in the female subjects hold for men also? How do the male subjects as a group differ from the female subjects as a group?

c) Body mass and metabolic rate. Exercise (b) gives data on the lean body mass and metabolic rate for 12 women and 7 men.

(1) Using the scatter plot you constructed for the previous exercise do you think the correlation will be about the same for men and women or quite different for the two groups? Why?
(2) Calculate r for women alone and also for men alone. (Use the data analysis function in Excel for this calculation or a calculator that has a regression function)
(3) Calculate the mean body mass for the women and for the men. Does the fact that the men are heavier than the women on the average influence the correlations? If so, in what way?

d) Food poisoning. Below are data on 18 people who fell ill from an incident of food poisoning. The data give each person's age in years, the incubation period (the time in hours between eating the infected food and the first signs of illness), and whether the victim survived (S) or died (D).

Person : 1 2 3 4 5 6 7 8 9
Age 29 39 44 37 42 17 38 43 51
Incubation 13 46 43 34 20 20 18 72 19
Outcome D S S D D S D S D

Person 10 11 12 13 14 15 16 17 18
Age 30 32 59 33 31 32 32 36 50
Incubation 36 48 44 21 32 86 48 28 16
Outcome D D S D D S D S D

(1) Create an Excel spreadsheet of the data and use the chart wizard to construct a scatter plot of incubation period against age, using different symbols for people who died and those who survived.
(2) Is there an overall relationship between age and incubation period? If so, describe it.
(3) More important, is there a relationship between either age or incubation period and whether the victim survived? Describe any relationships that seem important here.
(4) Are there any unusual cases that may require individual investigation?

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