Body mass index (BMI) is a measure of body fat based on height and weight. According to the document Dietary Guidelines for Americans, published by the U.S. Department of Agriculture and the U.S. Department of Health and Human Services, for adults, a BMI of greater than 25 indicates an above healthy weight (i.e., overweight or obese). Of 750 randomly selected adults whose highest degree is a bachelor’s, 386 have an above healthy weight; and of 500 randomly selected adults with a graduate degree, 237 have an above healthy weight.
a. What assumptions are required for using the two-proportions z-test here?
b. Apply the two-proportions z-test to determine, at the 5% significance level, whether the percentage of adults who have an above healthy weight is greater for those whose highest degree is a bachelor’s than for those with a graduate degree.
c. Repeat part (b) at the 10% significance level. In Exercises 11.94–11.99, apply Procedure 11.4 on page 465 to find the required confidence interval.