(Section 9.3) Does how long young children remain at the lunch table help predict how much they eat? Here are summary statistics and a scatterplot with regression line for data based on 20 toddlers observed over several months at a nursery school. "Time" is the average number of minutes a child spent at the table when lunch was served. "Calories" is the average number of calories the child consumed during lunch, oes calculated from careful observation of what the child ate each day. 8 Statistic Time Cal Mean 34.010 456.000 460 Standard Deviation 6.316 29.940 440 Sample Size 20 420 Correlation -0.649 Slope -3.077 200 35 40 Intercept 560.651 Time Is there evidence of a correlation between time spent at the table and number of calories consumed? Write hypotheses, find a p-value using the distribution, and write a conclusion in context. 30 20 10 0.6 0.4 0.2 0.2 0.4 0.6 b. A 95% prediction interval (PI) taken at 35 minutes at the table is (402.551, 503.356). Interpret the prediction interval. c. A 95% confidence interval (CI) taken at 35 minutes at the table is (441.821, 464.087). Interpret the confidence interval. d. Following are two intervals for toddlers who spend 40 minutes at the table. Indicate which is the prediction interval and which is the confidence interval for the mean. Explain. (422.232, 452,904) (386.074, 489.063)