Question bank / Evaluating statistical claims: observational studies and experiments

Math · Problem-Solving and Data AnalysisHard

At a school of 800800 students, 680680 students order lunch with a new app and the other 120120 students order at the counter. Last month, 4040 students received a wrong lunch order, and 3030 of those 4040 students had ordered with the app. A parent claims that because most wrong orders came from app users, the app makes a wrong order more likely. Which of the following best evaluates the claim?

A

The claim is supported, because 75%75\% of the wrong orders came from app users.

B

The claim is supported, because more students use the app than order at the counter.

C

The claim is not supported, because 4040 wrong orders is only 5%5\% of all students.

D

The claim is not supported, because about 4.4%4.4\% of app users and about 8.3%8.3\% of counter users received a wrong order.

Show answer and explanation

Answer: D

Most wrong orders came from app users because most students use the app. To compare, use rates. Of the app users, 30680≈4.4%\frac{30}{680} \approx 4.4\% received a wrong order, while 10120≈8.3%\frac{10}{120} \approx 8.3\% of counter users did. App users were actually less likely to receive a wrong order.

Choice A uses the share of wrong orders from app users, which mostly reflects how many students use the app, not how likely each app user is to get a wrong order.

Why the other choices are wrong

  • A. Most wrong orders came from app users because most students use the app. Compare rates instead.
  • B. The number of app users explains why there are more wrong app orders, not whether the app makes errors more likely.
  • C. The overall error rate doesn't compare app users with counter users.
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