AP Statistics: Lesson 7.01 Problem According to the U.S. FDA, more than 1 in 3 Americans are following a specific diet or eating pattern. For 2020, the FDA claims the following percentages for U.S. adults: Diet "Clean Intermittent Gluten Low-Carb Plant- Standard Eating" Fasting -Free American Based Diet Percent of 10% 9% 6% 6% 5% 64% U.S. Adults A college professor randomly sampled 384 undergraduate students to determine at a=0.05 whether the distribution of eating habits for undergraduate students at this university differs from the FDA claim. The sample data is shown in the table below. Diet "Clean Intermittent Gluten Low-Carb Plant- Standard Eating" Fasting -Free American Based Diet Sample 52 40 12 27 25 228 1. Write the appropriate null and alternative hypotheses for a Goodness of Fit test: (2pts) Ho: HA:2. Calculate the Expected Counts and verify the assumptions for inference: (9 pts) Diet "Clean Intermittent Gluten Low-Carb Plant- Standard Eating" Fasting -Free American Based Diet Sample 52 40 12 27 25 228 Expected Independence: Large Counts: 3. Calculate the test statistic and p-value for the Goodness of Fit test. (2 pts) Test Statistic: p-value: 4. Write an appropriate conclusion: (2pts)5. The following chart shows the contributed value of X2 from each category. Which categories are most out of line with the FDA claim? How are they different? Which categories are most similar to the FDA Claim? {5 pts) Chart of Contribution to the Chi-Square Value by Category Contributed Value 9 d M H