Question 34·Easy·Inference from Sample Statistics and Margin of Error
A random sample of customers at a café showed an average waiting time of 8.2 minutes, with an associated margin of error of 0.6 minute. Which statement is best supported about the mean waiting time for all customers at the café?
For questions about a sample mean and a margin of error, immediately think "mean ± margin of error." Subtract the margin of error from the sample mean to get the lower bound, and add it to get the upper bound. Then quickly scan the choices for the one that describes the mean as lying within that full interval (not just less than one endpoint or greater than the other). This approach is fast and avoids overthinking the statistics background during the test.
Hints
Think about what margin of error means
Margin of error tells you how far the true population mean could be above or below the sample mean. So you should both subtract and add this number to the sample mean.
Find the two endpoints
Compute and . These give the smallest and largest reasonable values for the mean waiting time of all customers.
Compare with the choices
Look for the choice that describes the mean as lying between the two numbers you just found, not strictly less than or greater than one of them.
Desmos Guide
Compute the lower bound
In Desmos, type 8.2 - 0.6 and press Enter. Note the value you get; this is the lower end of the interval for the mean waiting time.
Compute the upper bound and match the choice
Next, type 8.2 + 0.6 and press Enter. This result is the upper end of the interval. Choose the answer option that says the mean waiting time is between these two Desmos results.
Step-by-step Explanation
Interpret the margin of error
The sample shows an average (mean) waiting time of minutes and a margin of error of minute.
Margin of error means the true mean for all customers is likely within minute above or below the sample mean.
Compute the lower and upper bounds
To find the possible range for the population mean:
- Lower bound: subtract the margin of error from the sample mean: .
- Upper bound: add the margin of error to the sample mean: .
So the mean for all customers is likely between those two numbers.
Match the interval to an answer choice
From step 2, the interval is from minutes up to minutes.
The statement that matches this is: It is between 7.6 and 8.8 minutes.