The paper “Effects of Fast-Food Consumption on Energy Intake and Diet Quality Among Children in a National Household Survey” (Pediatrics [2004]: 112– 118) investigated the effect of fast-food consumption on other dietary variables. For a sample of 663 teens who reported that they did not eat fast food during a typical day, the mean daily calorie intake was 2258 and the sample standard deviation was 1519. For a sample of 413 teens who reported that they did eat fast food on a typical day, the mean calorie intake was 2637 and the standard deviation was 1138.
a. What assumptions about the two samples must be reasonable in order for the use of the two-sample t confidence interval to be appropriate?
b. Use the given information to estimate the difference in mean daily calorie intake for teens who do eat fast food on a typical day and those who do not.