Bluebook SAT Test Inference from Sample Statistics and Margin of Error 9

Question 1

A random sample of 500 households in a county found that 38% have solar panels installed, with a margin of error of ±4 percentage points at 95% confidence. Which of the following intervals represents the plausible range for the true proportion of all county households with solar panels?

Accepted Answer

34% to 42%

Answer

The confidence interval is formed by adding and subtracting the margin of error from the sample proportion: 38% ± 4% gives 34% to 42%.

Question 2

A research team surveys 900 randomly selected adults and finds that 61% support a proposed policy. The team then conducts a second survey using a random sample of 225 adults. Assuming the true proportion stays the same, how does the margin of error for the second survey compare to the first?

Accepted Answer

It doubles

Answer

Margin of error is proportional to 1/√n; reducing n from 900 to 225 (dividing by 4) doubles 1/√n, so the margin of error doubles.

Question 3

A 95% confidence interval for the mean hours of weekly exercise among adults in a city is (3.1 hours, 4.5 hours). A fitness company claims the true mean is 5 hours per week. Which statement best evaluates this claim?

Accepted Answer

The claim is inconsistent with the data because 5 hours is outside the confidence interval.

Answer

Because 5 hours falls outside the 95% confidence interval of (3.1, 4.5), the data do not support the company's claim.

Question 4

A school principal wants to estimate the proportion of students who walk to school. She surveys a random sample of 50 students and obtains a margin of error of ±7%. If she wants to reduce the margin of error to ±3.5%, approximately how large must the new sample be?

Accepted Answer

200

Answer

Halving the margin of error requires quadrupling the sample size; 50 × 4 = 200.

Question 5

In a study of 800 randomly chosen shoppers, 44% said they prefer buying groceries online. The reported margin of error is ±3.5 percentage points at 95% confidence. A store manager claims that fewer than 40% of shoppers prefer online grocery shopping. Which statement best assesses this claim?

Accepted Answer

The claim is plausible because 40% falls just inside the lower boundary of the confidence interval.

Answer

The 95% CI is approximately 40.5% to 47.5%, so 40% barely falls outside it, making the manager's claim not well-supported by the data.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Inference from Sample Statistics and Margin of Error 9