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

The interval becomes narrower.

Answer

The interval stays the same.

Answer

The interval shifts to the right.

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

(3.06, 3.14)

Answer

(3.00, 3.20)

Answer

(2.90, 3.30)

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 claim is false because the sample proportion is 72%.

Answer

The claim is plausible because 68% equals the lower bound.

Answer

The claim is not plausible because 68% falls below the lower bound of 68%.

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

41%

Answer

47%

Answer

44%

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

The second sample has a larger margin of error because more data introduces more uncertainty.

Answer

Both estimates have the same margin of error since the means are similar.

Answer

The first sample is more reliable because smaller samples are more tightly controlled.

Question 6

A study reports a 95% confidence interval for mean sleep duration of (6.8 hours, 7.6 hours). A health agency claims adults should sleep at least 7.5 hours on average. Which statement is best supported by the interval?

Accepted Answer

The agency's recommendation of 7.5 hours is a plausible population mean.

Answer

The agency's recommendation is not plausible given the data.

Answer

The true mean sleep duration is exactly 7.2 hours.

Answer

Adults are sleeping too little because the lower bound is 6.8 hours.

Question 7

A school's random survey of 100 students estimates that the mean time spent on homework is 2.4 hours with a margin of error of ±0.3 hours at 95% confidence. What additional information is needed to determine whether the true mean exceeds 2.5 hours?

Accepted Answer

Whether 2.5 falls within or outside the confidence interval

Answer

The exact standard deviation of the sample

Answer

The number of teachers who assign homework

Answer

The median homework time, not just the mean