A poll’s margin of error helps turn a sample percentage into a plausible range for the population percentage. When the margin is given in percentage points, subtract and add that number of points. Then look for a conclusion about the population that allows uncertainty: a sample estimate does not establish the exact population percentage.
Hints
- Hint 1
A sample is the people surveyed; the population is the larger group the poll aims to describe. The sample percentage estimates the population percentage, but does not fix it exactly. Which group should the conclusion describe?
- Hint 2
A percentage point is a direct difference between percentages: to is point. To find the lower end of the plausible range, subtract the stated margin from the sample percentage.
- Hint 3
A plausible interval extends the same number of points below and above the estimate. After finding the lower end, add the margin to find the upper end. Which wording treats that range as plausible rather than certain?
Step-by-step
Build and interpret the plausible interval
Step 1Connect the sample to the county
No Desmos needed. Each endpoint takes one subtraction or addition. The sample is the adults surveyed; the population is all adults in River County. Because the adults were randomly selected, the sample’s supports an estimate for that population, not an exact countywide percentage.
- Step 2
Find the lower end
A margin of error of percentage points means moving points from the estimate. Subtract the points directly, not of . Find the lower end:
- Step 3
Find the upper end
The margin extends equally in the other direction. Find the upper end by adding percentage points:
- Step 4
Choose a conclusion that allows uncertainty
A 95% confidence level describes a method that captures the true population percentage in about of repeated random polls. It does not guarantee an exact value from this poll. So it is plausible that between and of all adults in River County support the tax. Choice D.