Question 40·Easy·Inference from Sample Statistics and Margin of Error
A nutritionist recorded the sugar content of randomly selected energy bars of a certain brand. The mean sugar content was estimated to be grams, with an associated margin of error of gram. Which of the following is a plausible statement about the mean sugar content of all energy bars of this brand?
When a question gives a sample mean and a margin of error, immediately form an interval by doing estimate minus margin and estimate plus margin. That interval represents the plausible values for the population mean, so scan the choices for the one that says the true mean is between those two bounds, and beware of answers that only say “less than” or “greater than” one bound or that describe being outside the interval instead of inside it.
Hints
What does the margin of error do?
Think about what information the margin of error adds to the estimated mean of grams. How does it tell you how far off the estimate might be?
Turn mean ± margin into a range
Use the estimated mean and the margin of error to form a range by calculating and .
Compare your range to the choices
Once you know the lower and upper numbers in your range, look for the choice that describes the mean of all bars as being within that interval, not only below it or only above it.
Desmos Guide
Compute the lower bound
In one Desmos expression line, type 18.6 - 0.9 and note the numerical output; this is the lower end of the plausible interval for the mean.
Compute the upper bound
In a new line, type 18.6 + 0.9 and note the output; this is the upper end of the plausible interval for the mean.
Match to the answer choices
Look at the two numbers Desmos gave you and select the option that states the mean sugar content of all bars is between those two values (not only less than one or greater than the other).
Step-by-step Explanation
Interpret the mean and margin of error
The nutritionist’s sample gives an estimated mean sugar content of grams. The margin of error of gram means the true mean for all bars is expected to be within gram above or below .
So we form an interval using:
- lower bound:
- upper bound:
Calculate the lower bound of the interval
Find how low the true mean might reasonably be by subtracting the margin of error from the estimated mean:
So the lower end of the plausible interval is grams.
Calculate the upper bound of the interval
Find how high the true mean might reasonably be by adding the margin of error to the estimated mean:
So the upper end of the plausible interval is grams.
Match the interval to the answer choices
The plausible values for the true mean sugar content lie between grams and grams. The only choice that states this two-sided interval is:
It is between grams and grams.