A study of fast-food intake is described in the paper "What People Buy From
Fast-Food Restaurants" (Obesity [2009]:1369-
1374). Adult customers at three hamburger chains (McDonald's, Burger King, and
Wendy's) in New York City were approached as they entered the restaurant at
lunchtime and asked to provide their receipt when exiting. The receipts were
then used to determine what was purchased and the number of calories consumed
was determined. In all, 3,857 people participated in the study. The sample
mean number of calories consumed was 857 and the sample standard deviation was
677 .
a. The sample standard deviation is quite large. What does this tell you about
number of calories consumed in a hamburgerchain lunchtime fast-food purchase
in New York City?
b. Given the values of the sample mean and standard deviation and the fact
that the number of calories consumed can't
be negative, explain why it is not reasonable to assume that the distribution
of calories consumed is normal.
c. Based on a recommended daily intake of 2,000 calories, the online Healthy
Dining Finder (www.healthydiningfinder .com) recommends a target of 750
calories for lunch. Assuming that it is reasonable to regard the sample of
3,857 fast-food purchases as representative of all hamburger-chain lunchtime
purchases in New York City, carry out a hypothesis test to determine if the
sample provides convincing evidence that the mean number of calories in a New
York City hamburger-chain lunchtime purchase is greater than the lunch
recommendation of 750 calories. Use \(\alpha=0.01\).
d. Would it be reasonable to generalize the conclusion of the test in Part (c)
to the lunchtime fast-food purchases of all adult Americans? Explain why or
why not.
e. Explain why it is better to use the customer receipt to determine what was
ordered rather than just asking a customer leaving the restaurant what he or
she purchased.
