Bluebook SAT Test Inference from Sample Statistics and Margin of Error 5

Question 1

The table below shows results from two surveys about a proposed tax increase:

Survey X: 600 respondents, 54% in favor, margin of error ±4%
Survey Y: 150 respondents, 58% in favor, margin of error ±8%

Which survey provides a more precise estimate of the proportion in favor, and why?

Accepted Answer

Survey X, because a larger sample produces a smaller margin of error.

Answer

Survey X uses a larger sample (600 vs. 150), yielding a smaller margin of error (±4% vs. ±8%), making it more precise.

Question 2

A study estimates that the mean annual income of workers in an industry is $52,000, with a 95% confidence interval of ($49,500, $54,500). A labor economist claims the true mean income in that industry is $55,000. Which evaluation is most appropriate?

Accepted Answer

The claim is not supported because $55,000 falls above the upper bound of the interval.

Answer

Since $55,000 is above the upper bound of $54,500, it falls outside the confidence interval and is not a plausible value for the true mean.

Question 3

A polling agency surveys 1,600 likely voters and reports that 49% plan to vote for a candidate, with a margin of error of ±2.5 percentage points. Which conclusion is best supported?

Accepted Answer

A majority support could exist because the confidence interval extends above 50%.

Answer

The confidence interval is 46.5%–51.5%; since this range includes values above 50%, majority support is a plausible population outcome.

Question 4

A sample of 400 college students finds that 30% own a car. If the margin of error is ±4%, what is the 95% confidence interval, and which value is consistent with the population proportion?

Accepted Answer

26%–34%; a true proportion of 31% is plausible.

Answer

The confidence interval is 30% ± 4% = 26%–34%; 31% falls within this range and is therefore a plausible population proportion.

Question 5

To estimate the average price of a gallon of milk in a large city, an economist samples 100 stores and finds a mean of $3.85 with a margin of error of ±$0.20 at 95% confidence. If she wants the margin of error to be ±$0.10, approximately how many stores must she sample?

Accepted Answer

400 stores

Answer

To halve the margin of error, you must quadruple the sample size (since MoE ∝ 1/√n): 100 × 4 = 400 stores.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Inference from Sample Statistics and Margin of Error 5