Bluebook SAT Test Inference from Sample Statistics and Margin of Error 4

Question 1

A researcher conducts a study and finds a 90% confidence interval for the mean is (55, 65). If the researcher recalculates using a 95% confidence level with the same data, what happens to the interval?

Accepted Answer

The interval becomes wider.

Answer

Higher confidence levels require wider intervals to capture the true parameter with greater certainty, so a 95% interval is wider than a 90% interval for the same data.

Question 2

A random sample of 225 students finds a mean GPA of 3.1 with a standard error of 0.04. What is the 95% confidence interval for the mean GPA, given that the critical value is approximately 2?

Accepted Answer

(3.02, 3.18)

Answer

The 95% confidence interval is 3.1 ± 2(0.04) = 3.1 ± 0.08, giving the range (3.02, 3.18).

Question 3

A market research firm surveys 500 randomly selected shoppers. The survey estimates that 72% prefer Brand A, with a margin of error of ±4%. A competitor claims that fewer than 68% of shoppers prefer Brand A. Which statement best evaluates this claim?

Accepted Answer

The claim is plausible because 68% is within the confidence interval.

Answer

The confidence interval is 68%–76%; since 68% is the lower bound of the interval, it is a plausible population value, making the competitor's claim possible.

Question 4

In a poll of 800 randomly selected adults, 44% said they regularly recycle, with a margin of error of ±3.5 percentage points. Which value is NOT in the 95% confidence interval?

Accepted Answer

40%

Answer

The 95% confidence interval is 40.5%–47.5%; 40% is below the lower bound and therefore not in the interval.

Question 5

A biologist samples 36 rabbits from a large population and finds a mean ear length of 8.4 cm. She increases her sample to 144 rabbits, finding essentially the same mean. Which statement about the two estimates is true?

Accepted Answer

The second sample has a smaller margin of error because the sample size is four times larger.

Answer

Quadrupling the sample size (36 to 144) halves the margin of error since margin of error ∝ 1/√n.

Bluebook SAT Practice Test

Bluebook SAT Practice Test

Bluebook SAT Test Inference from Sample Statistics and Margin of Error 4