Directions: Provide the required answers for each question in an Excel or Word document, making sure to annotate which question is being answered. The dataset, fram_samp2.xls, is a subset of the data from the Framingham Heart Study, a longitudinal study to assess risk factors for cardiovascular disease. It includes n=4,434 participants who completed one of the regularly scheduled examinations from 1956-1968. The following table shows variable names, as they appear in the dataset, along with brief descriptions and coding details for each variable.
Variable Name Description Coding
RANDOM ID Random, unique number for each participant 2448-9999312
OBESE Classified as obese with a Body mass index > 30 0=no, 1=yes
DIABETES Diabetic 0=no, 1=yes
DAYS TO DEATH Number of days from exam to death* 0-8766 *If participant did not die, number of days is end of follow-up period (8766 days=24 years) or last known contact date
Physicians are interested in studying the effects of obesity on the health of the Framingham population. Using the sample provided, answer the questions below.
1. Nationally, 37.8% of the people in the United States are obese. Determine if the proportion of people who are obese in the Framingham population differs from the rest of the country by calculating the proportion and two-sided 95% confidence interval for the sample. (10 points)
2. Around 10.7% of the people in the United States are diabetic. Is the proportion of people who are diabetic in the Framingham sample different from this national value? Determine this by calculating the proportion for the Framingham sample and its two-sided 95% confidence interval. (10 points)
3. Physicians believe that obesity and diabetes are related. Using the sample of subjects from Framingham, determine if being obese and having diabetes are independent. Use a significance level of α=0.05.
a. State your null and alternative hypotheses (3 points)
b. Calculate the appropriate test statistic. (9 points)
c. Explain the results in a way that the physicians will be able to understand it. (3 points)
4. The physicians also believe that people who are obese are more likely to die earlier than those who are not. Again use the data in the Framingham sample to test this theory by comparing the mean number of days until death for the two groups. Use a significance level of α=0.05.
a. State your null and alternative hypotheses (3 points)
b. Calculate the appropriate test statistic. (9 points)
c. Explain the results in a way that the physicians will be able to understand it. (3 points)