Question

In: Statistics and Probability

A randomized study was performed to determine whether a diet of processed meats causes a higher...

A randomized study was performed to determine whether a diet of processed meats causes a higher proportion of incidents of breast cancer. Researchers compared high intake versus low intake diets of processed meats for women with breast cancer and found the following results shown in the two-way table below:

Breast Cancer

No Breast Cancer

Total

High Intake processed meat

88

152

240

Low Intake processed meat

61

159

220
  1. Using phigh for the proportion with diet high in processed meat who got breast cancer and plow for the proportion of women with diet low in processed meat who got breast cancer, compute the appropriate sample statistic for this difference of proportions. Show notation and the calculation.
  2. Use STATKEY with bootstrapping to create 10,000 generated samples. Use the STATKEY output to find the 95% confidence interval. Then sketch the curve (no details) for what you see in the STATKEY output. Be sure to write the lower and upper bound values on your curve.
  3. Interpret these results in context of the problem.
  4. Now formulate the null and alternative hypotheses to determine whether there is a difference in proportions for women to get breast cancer depending on high or low intake of processed meats.

Solutions

Expert Solution

(a) phigh = 88/240 = 0.37

plow = 61/220 = 0.28

p = 0.37*240 + 0.28*220/(240 + 220) = 0.32

(b) The STATKEY output is:

The curve is:

The 95% confidence interval for the difference of proportions is between 0.0933 and 0.2559.

(c) We are 95% confident that the true difference of proportions is between 0.0933 and 0.2559.

(d) The hypothesis being tested is:

H0: p1 = p2

Ha: p1 ≠ p2

orchestra answered 1 year ago
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