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# Statistics Problem Set: Diabetes and Weight

1. In a study of the effects of diet on diabetes, subjects put on one of three diets: (i) Mediterranean diet (more vegetables, olive oil, less meat), (ii) low-carb diet or (iii) unrestricted (subjects may eat what they typically eat).

The following was observed from the study:
- 40.1% of those in an unrestricted diet developed diabetes. That figure amounted to 51.74% of those who ultimately suffered from the diabetes.
- 78.15% of those in a low-carb diet did not get diabetes. That is the equivalent of 25.38% of the total number of subjects.

Mediterranean Low-Carb Unrestricted
Diabetes 89
No diabetes 186
Total

Use the study details to fill in all the missing values in the above table.

2. Here is a two-way table of the number of adults in the United States (in thousands) classified by age group and weight category based on body mass index (BMI).

Underweight Healthy weight Overweight Obese
18 to 44 years 2,325 43,277 33,863 25,835
45 to 64 years 753 21,871 27,708 21,803
65 to 74 years 248 5,702 7,194 4,907
75 years and over 597 6,756 5,861 2,837

The total counts in each age group are very different, so it is important to use percents rather than counts in comparing them. Find the conditional distribution of weight category given the age group. Use your results to describe the obesity crisis in the four age groups.

#### Solution Preview

1.
Mediterranean Low-Carb Unrestricted
Diabetes 31 52 89
No diabetes 242 186 133
Total 273 238 222

For the low-carb, the total is ...

#### Solution Summary

Diabetes and weight is examined for statistics in the solution.

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