Question 33·Hard·Evaluate Statistical Claims: Observational Studies and Experiments
A coffee-shop chain claims that the mean time a customer waits in line before placing an order at any of its locations is no more than 4 minutes. To investigate this claim, an employee recorded the wait times of the first 40 customers who arrived at one of the chain's downtown locations between 7:00 a.m. and 8:00 a.m. on a weekday. The mean wait time for these 40 customers was 5.3 minutes.
Which of the following statements best evaluates whether the employee's data provide convincing evidence that the chain's claim is false?
For SAT questions about evaluating statistical claims, first identify the population (who the claim is about) and the sample (who was actually observed). Then focus on how the sample was collected: Is it random and from the whole population, or is it limited to one location, time, or type of person? Be skeptical of choices that draw strong conclusions ("must be false," "definitely true") from a single, possibly biased sample, or that rely only on sample size without mentioning representativeness. Also, ignore distractions like extra statistics (median vs. mean) if they are not central to the claim being tested.
Hints
Identify population vs. sample
Ask yourself: What group is the chain’s claim about, and which group did the employee actually collect data from?
Think about representativeness
Compare "any of its locations" to "first 40 customers at one downtown location between 7:00 a.m. and 8:00 a.m."—does this sample seem like it represents all customers?
Evaluate what each choice is focusing on
As you read each option, ask: Is it focusing on the size and method of the sample (how the data were collected), or is it jumping straight to a conclusion from one sample value?
Consider whether extra statistics are really needed
The claim is about the mean wait time. Think about whether other statistics (like the median) are necessary to make any judgment at all about that claim.
Step-by-step Explanation
Clarify the claim and what the data show
The chain’s claim is about all customers at any of its locations: it says the population mean wait time is no more than 4 minutes (mean wait time ). The employee’s data are from 40 customers at one downtown location between 7:00 a.m. and 8:00 a.m. on one weekday, and their sample mean wait time is 5.3 minutes.
Recall what makes evidence convincing in statistics
To use a sample to judge a claim about a whole population, the sample needs to be representative of that population. On the SAT, that usually means something close to a random sample from the whole group you care about (here: all customers at all locations and times). If the sampling method is biased (systematically favors certain types of customers or times), then the sample results may not match the population.
Examine how the sample was collected
The employee did not randomly sample from all customers. Instead, they took the first 40 customers at one downtown location during the morning rush hour (7–8 a.m.). Customers at that location and time may have longer-than-average waits (for example, due to commuter crowds) compared with other times of day or other locations. So the sample may overestimate the typical wait for all customers.
Match the reasoning to the answer choices
Choices A and C both claim we can confidently say the chain’s claim is false just because the sample mean is higher and/or the sample size is 40, but they ignore the likely sampling bias and the lack of a random, representative sample. Choice D focuses on the median, which is not needed to evaluate a claim about the mean and misses the real problem. Choice B correctly explains that because the data come only from early-morning customers at a single location, the sampling method may be biased and the results may not represent all customers, so the data do not provide convincing evidence that the chain’s claim is false.