Question

Consumption of fast food is a topic of interest to researchers in the field of nutrition. The article "Effects of Fast-Food Consumption on Energy Intake and Diet Quality Among Children" (Pediatrics [2004]: \(112-118\) ) reported that 1720 of those in a random sample of 6212 U.S. children indicated that on a typical day they ate fast food. Estimate \(\pi\), the proportion of children in the U.S. who eat fast food on a typical day.

Short answer

The estimated proportion (\(\pi\)) of U.S. children who eat fast food on a typical day is approximately \(0.277\) (or 27.7%), based on the provided sample.

Step-by-step solution

Understanding given data

We are given that in a sample of 6212 U.S. children, 1720 of them eat fast food on a typical day. The goal is to estimate the proportion (\(\pi\)) of all U.S. children who are likely to consume fast food in a typical day based on this sample.

Calculate the Proportion

The proportion (\(\pi\)) of children who eat fast food is calculated by dividing the number of children who eat fast food by the total number of children. In this case, \(\pi\) can be calculated as: \(\pi = 1720 / 6212\).

Calculation

Perform the division operation that was established in the previous step to get the estimate of \(\pi\).