Bluebook SAT Test Inference from Sample Statistics and Margin of Error 3

Question 1

A researcher wants to estimate the mean weight of a species of fish in a lake. Sample 1 consists of 50 randomly caught fish and sample 2 consists of 200 randomly caught fish. Both samples have similar means. Which sample will produce a confidence interval with a smaller width?

Accepted Answer

Sample 2, because larger samples produce narrower confidence intervals.

Answer

Larger samples reduce the standard error, resulting in narrower confidence intervals and more precise estimates.

Question 2

The results of a study report: 'We are 95% confident that the mean number of hours adults spend reading per week is between 3.2 and 4.8 hours.' What is the margin of error?

Accepted Answer

0.8 hours

Answer

The margin of error is half the confidence interval width: (4.8 − 3.2)/2 = 0.8 hours.

Question 3

A random sample of 64 students shows a mean study time of 3.5 hours per day with a standard deviation of 1.2 hours. If the sample size is increased to 256 students with the same standard deviation, by what factor does the margin of error change?

Accepted Answer

It is divided by 2.

Answer

Sample size increases by a factor of 4 (64 to 256), so √4 = 2; the margin of error is divided by 2.

Question 4

A television network surveys 1,000 randomly selected viewers and reports that 63% watch a particular show, with a margin of error of ±3 percentage points at 95% confidence. Which of the following populations can this estimate validly be generalized to?

Accepted Answer

All viewers in the population from which the random sample was drawn

Answer

Inferences from a random sample can only be generalized to the population from which that sample was drawn, not to broader populations not represented.

Question 5

A poll estimates that 48% of voters support a candidate, with a margin of error of ±4 percentage points. A competitor's poll estimates 51% support with a margin of error of ±4 percentage points. Which conclusion is most appropriate?

Accepted Answer

The results are consistent because the confidence intervals overlap.

Answer

Poll 1 gives 44%–52% and Poll 2 gives 47%–55%; these intervals overlap, so both results are consistent with a range of true values.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Inference from Sample Statistics and Margin of Error 3