Question 11·Medium·Inference from Sample Statistics and Margin of Error
A polling organization selected a random sample of 600 voters from a large city and found that the mean amount of time the respondents spent reading news online each day was minutes, with a margin of error of minutes.
Which of the following statements is the most appropriate conclusion?
For margin-of-error questions, first identify the sample statistic (mean or proportion) and the size of the margin of error, then quickly form the interval using "estimate ± margin of error." Interpret this interval as a plausible range for the population parameter, not a guarantee or a statement about individual values. On the SAT, be wary of answer choices using absolute language like "certain," "exactly," or those that talk about every single individual instead of the mean or proportion; the correct choice usually uses softer language such as "reasonable" or "plausible" and refers specifically to the population mean or proportion.
Hints
Think about what a margin of error represents
Ask yourself: Does a margin of error guarantee an exact value, or does it give a range of values that are considered reasonable for the true mean?
Use the margin of error with the sample mean
Combine the mean minutes with the margin of error minutes to find the low and high ends of a reasonable range for the mean time for all voters.
Pay attention to strong words like "certain" and "exactly"
In statistics questions, be careful with answer choices that claim absolute certainty or an exact population value when you are only given a sample and a margin of error.
Desmos Guide
Compute the endpoints of the interval
In Desmos, type 38-4 and 38+4 (either as two separate expressions or together as a list like {38-4, 38+4}). Note the two numerical results; these are the lower and upper bounds of the reasonable range for the population mean implied by the data.
Connect the numerical interval to the wording
Look at the numbers you got in Desmos and remind yourself that this range applies to the mean for all voters, based on sample data with uncertainty. Then choose the option whose wording best reflects a plausible range for the population mean, without claiming certainty, exactness, or limits on every individual.
Step-by-step Explanation
Interpret the statistics in the prompt
The problem says a random sample of 600 voters had a mean of minutes reading news online per day, with a margin of error of minutes.
- The sample mean ( minutes) is the average for the 600 people surveyed.
- The margin of error ( minutes) tells us how far the true population mean might reasonably be from the sample mean, in either direction.
Find the interval given by the margin of error
Use the margin of error to create a range around the sample mean:
- Lower end: minutes
- Upper end: minutes
So the margin of error suggests that the true mean time for all voters is likely to be somewhere between 34 and 42 minutes per day.
Match this idea to the correct wording
Now compare each choice to what a margin of error really means:
- Choice A says it is certain the mean is between 34 and 42 minutes. Statistics with a margin of error do not give absolute certainty, only a likely range.
- Choice B talks about each individual voter being between 34 and 42 minutes. The margin of error is about the overall mean, not about every single person's time.
- Choice C says the population mean is exactly 38 minutes. The margin of error tells us the true mean may differ from 38 by up to about 4 minutes, so we cannot claim it is exactly 38.
- Choice D correctly states that it is plausible (reasonable or likely) that the true mean is between 34 and 42 minutes.
Therefore, the best conclusion is: It is plausible that the actual mean daily time all voters in the city spend reading news online is between 34 and 42 minutes.