Bluebook SAT Test Inference from Sample Statistics and Margin of Error 5

Question 1

The table below shows results from two surveys about a proposed tax increase:

Survey X: 600 respondents, 54% in favor, margin of error ±4%
Survey Y: 150 respondents, 58% in favor, margin of error ±8%

Which survey provides a more precise estimate of the proportion in favor, and why?

Accepted Answer

Survey X, because a larger sample produces a smaller margin of error.

Answer

Survey Y, because a higher percentage supports the tax increase.

Answer

Survey Y, because it was conducted more recently.

Answer

Both surveys are equally precise since both use random sampling.

Question 2

A study estimates that the mean annual income of workers in an industry is $52,000, with a 95% confidence interval of ($49,500, $54,500). A labor economist claims the true mean income in that industry is $55,000. Which evaluation is most appropriate?

Accepted Answer

The claim is not supported because $55,000 falls above the upper bound of the interval.

Answer

The claim is supported because $55,000 is close to the upper bound.

Answer

The claim is supported because the sample mean is below $55,000.

Answer

The claim cannot be evaluated from a confidence interval alone.

Question 3

A polling agency surveys 1,600 likely voters and reports that 49% plan to vote for a candidate, with a margin of error of ±2.5 percentage points. Which conclusion is best supported?

Accepted Answer

A majority support could exist because the confidence interval extends above 50%.

Answer

The candidate will lose because fewer than 50% support her.

Answer

Exactly 49% of all likely voters plan to vote for the candidate.

Answer

The margin of error means the result is not statistically significant.

Question 4

A sample of 400 college students finds that 30% own a car. If the margin of error is ±4%, what is the 95% confidence interval, and which value is consistent with the population proportion?

Accepted Answer

26%–34%; a true proportion of 31% is plausible.

Answer

26%–34%; a true proportion of 35% is plausible.

Answer

28%–32%; a true proportion of 27% is not plausible.

Answer

26%–34%; a true proportion of 25% is plausible.

Question 5

To estimate the average price of a gallon of milk in a large city, an economist samples 100 stores and finds a mean of $3.85 with a margin of error of ±$0.20 at 95% confidence. If she wants the margin of error to be ±$0.10, approximately how many stores must she sample?

Accepted Answer

400 stores

Answer

200 stores

Answer

50 stores

Answer

800 stores

Question 6

A researcher reports that the 90% confidence interval for mean customer wait time is (4.2 min, 5.8 min). The 95% confidence interval using the same data would be:

Accepted Answer

Wider than (4.2 min, 5.8 min)

Answer

Narrower than (4.2 min, 5.8 min)

Answer

Identical to (4.2 min, 5.8 min)

Answer

Shifted higher than (4.2 min, 5.8 min)

Question 7

A random sample of 500 adults estimates that the mean number of books read per year is 12.4, with a standard error of 0.5. What is the approximate 95% confidence interval, using a critical value of 2?

Accepted Answer

(11.4, 13.4)

Answer

(12.0, 12.8)

Answer

(11.9, 12.9)

Answer

(10.4, 14.4)