For a sampling and generalization question, compare the group a claim describes with the people actually measured. Ask who could have been selected and whether that selection might favor certain customers. A sample mean describes the people sampled, but it may not represent the whole population. A large sample cannot fix a narrow sampling method.
Hints
- Hint 1
The target population is the whole group a claim describes. If a claim covers customers at any location, which customers would a sample need to represent?
- Hint 2
A convenience sample takes people who are readily available. Think about who the first customers during one morning hour leave out. Could wait times differ at other hours or locations?
- Hint 3
A sample mean is the average for the measured customers, not automatically the average for everyone. What does the reported average establish about those customers, and what would it take to extend that result?
Step-by-step
Check who the sample represents
Step 1Identify the group in the claim
No Desmos needed. The question is about who was sampled, not a calculation. The claim covers customers at any of the chain's locations, so the target population, the group the claim describes, extends beyond one shop.
- Step 2
Check how customers were selected
The employee measured the first 40 customers at one downtown shop during one weekday morning hour. This is a convenience sample: customers were included because they arrived there then, not because they were selected from customers across locations and times.
- Step 3
Interpret the reported average
The sample mean, or average for those measured, is minutes, which exceeds the claimed limit of minutes. So these 40 customers waited longer on average than the limit; that comparison alone doesn't establish the average for customers at other times or shops.
- Step 4
Decide whether the claim is disproved
Wait times could differ by hour or location, so this narrow sample may have selection bias: the way customers entered the sample may favor wait times unlike those across the chain. The data don't provide convincing evidence that the chain's broader claim is false. Choice B.