A sample mean is an average from the measured bars; it estimates the population mean, the average for all bars of that brand. A margin of error gives a plausible range for the population mean by extending below and above the estimate. The trap is to treat values outside that range as the plausible ones.
Hints
- Hint 1
The sample mean describes the bars that were measured. The population mean describes all bars of this brand. Which mean does the question ask you to make a statement about?
- Hint 2
A margin of error is an amount you move in both directions from an estimate. What do you get when you subtract it from the sample mean, and when you add it?
Step-by-step
Build the margin-of-error interval
Step 1Set up the plausible range
No Desmos needed. Each endpoint takes only one arithmetic operation. The randomly selected bars are the sample, the group that was measured. Their sample mean estimates the mean for all bars of this brand. A margin of error extends the estimate the same distance below and above it. So the plausible range for the population mean is to grams.
- Step 2
Find the two endpoints
Subtract the margin to find the lower endpoint:
Add it to find the upper endpoint:
- Step 3
Apply the range to the mean for all bars
The question asks about the population mean, not the sugar content of each bar. That mean for all bars is plausibly between grams and grams. Values outside those endpoints aren't supported by the given margin of error. Choice A.