Question: According to a recent report, 32.2% of American adults (aged 20 and older) are obese (The New York Times, August 15, 2008). Among ethnic groups in general, African-American women are more overweight than Caucasian women, but African-American men are less obese than Caucasian men. Sarah Weber, a recent college graduate, is curious to determine if the same pattern also exists in her hometown on the west coast. She randomly selects 220 African Americans and 300 Caucasian adults for the analysis. The following table contains the sample information.
a. Use the p-value approach to test if the proportion of obese African-American men is less than the proportion of obese Caucasian men at α = 0.05.
b. Use the critical value approach to test if the proportion of obese African-American women is more than the proportion of obese Caucasian women at α = 0.05.
c. Use the critical value approach to test if the proportion of obese African-Americans differs from the proportion of obese Caucasian adults at the 5% significance level.