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

36% to 40%

Answer

30% to 46%

Answer

38% 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

It is four times as large

Answer

It is halved

Answer

It stays the same

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

The claim is consistent with the data because 5 hours is close to the interval.

Answer

The claim cannot be evaluated without knowing the sample size.

Answer

The claim is consistent because 95% confidence intervals always include the true mean.

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

100

Answer

150

Answer

400

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 claim is definitively false because the sample proportion is above 40%.

Answer

The claim cannot be assessed without knowing the population size.

Answer

The claim is supported because the margin of error is larger than the difference.

Question 6

A 95% confidence interval for a population proportion is reported as (0.52, 0.68). What is the sample proportion and the margin of error?

Accepted Answer

Sample proportion = 0.60; margin of error = 0.08

Answer

Sample proportion = 0.52; margin of error = 0.16

Answer

Sample proportion = 0.68; margin of error = 0.08

Answer

Sample proportion = 0.60; margin of error = 0.16

Question 7

A researcher surveys a random sample of 1,024 adults and finds that 30% report feeling stressed daily, with a margin of error of ±3 percentage points at 95% confidence. If the researcher increases the sample to 4,096 adults, what would the new margin of error be, assuming the same proportion?

Accepted Answer

±1.5 percentage points

Answer

±6 percentage points

Answer

±3 percentage points

Answer

±0.75 percentage points