Question

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.

Short answer

The assumptions needed for the t test are that the two groups are independent, normally distributed, and have equal variances. The difference in mean daily calorie intake between teens who do eat fast food and those who don't is 379 calories.

Step-by-step solution

Identify the Assumptions for Two-Sample t Test

The assumptions needed for a two-sample t confidence interval to be appropriate include:1. The two populations (teens who eat fast food and those who do not) are independent. Essentially, someone from one population doesn't influence someone from another. 2. Both populations are normally distributed (or approximately so), but this is often relaxed if the sample sizes are relatively large.3. The variances of the two populations are equal. This can often be checked with a test for equality of variances.

Calculate the Difference in Mean Daily Calorie Intake

The mean daily calorie intake for teens who eat fast food is 2637 while for those who don't, it's 2258. So, the difference in mean daily calorie intake is \(2637 - 2258 = 379\) calories.