Question 8·Medium·Inference from Sample Statistics and Margin of Error
In a statewide survey, a research firm interviewed a random sample of 1,200 registered voters to estimate the proportion who support a proposed bond measure. The firm reported that 54% of the sampled voters support the measure, with an associated margin of error of 2.8%. Based on these results, which of the following is the most appropriate conclusion about the proportion of all registered voters in the state who support the bond measure?
For survey and margin-of-error questions, first identify the sample statistic (here, 54%) and the margin of error (2.8%). Quickly form the plausible interval for the population parameter by subtracting and adding the margin of error (54 − 2.8 and 54 + 2.8), then translate that interval into a verbal description. On the SAT, avoid choices that claim an exact population value or that use only one side of the interval ("at least" or "no more than") when a margin of error is given; the most appropriate conclusion usually describes a range of plausible values for the entire population.
Hints
Think about what margin of error means
The margin of error tells you how much higher or lower the true population proportion could reasonably be, compared with the sample proportion. Ask: How do I use it with the 54%?
Use the margin of error to form an interval
Take the reported 54% and both subtract 2.8 percentage points and add 2.8 percentage points. What two percentages do you get?
Compare your interval to the choices
Once you have the lower and upper bounds from the previous hint, look for the choice that talks about a range of plausible values for the population proportion, not a single exact number or just one-sided statements like "at least" or "no more than."
Desmos Guide
Use Desmos to compute the bounds of the interval
In Desmos, type 0.54 - 0.028 to find the lower bound and 0.54 + 0.028 to find the upper bound for the plausible population proportion. Interpret these two decimal outputs as percentages (multiply by 100) and then choose the answer option that correctly describes that full percentage range for the population proportion.
Step-by-step Explanation
Interpret the sample percentage and margin of error
The 54% is the proportion of the sample (the 1,200 voters surveyed) who support the measure. The margin of error of 2.8% tells you how far the true proportion of all registered voters might reasonably be from this sample estimate, in either direction (higher or lower).
Calculate the plausible range for the population proportion
To find the plausible range, subtract and add the margin of error to the sample percentage:
So, based on this survey, the true proportion of all registered voters who support the measure is reasonably likely to be between 51.2% and 56.8%.
Match this interpretation to the answer choices
We now look for the choice that correctly describes that the true support in the whole population could be anywhere between the lower bound, 51.2%, and the upper bound, 56.8%, rather than exactly one value or only above/below one bound. The answer that states "It is plausible that between 51.2% and 56.8% of registered voters support the bond measure" is therefore the most appropriate conclusion.