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

Sample 1, because smaller samples have less variability.

Answer

Both samples will produce intervals of equal width.

Answer

Sample 1, because it is easier to ensure a truly random sample.

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

1.6 hours

Answer

4.0 hours

Answer

3.2 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

It is multiplied by 4.

Answer

It is divided by 4.

Answer

It is multiplied 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

All viewers of all television networks worldwide

Answer

All 1,000 viewers who were surveyed

Answer

All adults who own a television

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

The second poll is more accurate because it shows higher support.

Answer

The two polls are contradictory and both should be discarded.

Answer

The candidate is guaranteed to lose because neither poll shows clear majority support.

Question 6

A company surveys 400 customers and finds a mean satisfaction score of 7.4 out of 10, with a margin of error of ±0.3. A manager claims the true mean satisfaction score is at most 7.0. Is this claim consistent with the survey?

Accepted Answer

No, because 7.0 is below the lower bound of the confidence interval.

Answer

Yes, because 7.0 is within one standard deviation of the mean.

Answer

Yes, because the company may have surveyed unsatisfied customers.

Answer

No, because the sample size of 400 is too small to trust.

Question 7

A study uses a random sample to estimate the proportion of adults in a county who exercise regularly. The 95% confidence interval is (0.34, 0.46). Which of the following must be true?

Accepted Answer

The sample proportion is 0.40.

Answer

Exactly 40% of adults in the county exercise regularly.

Answer

At least 95% of county adults exercise between 34% and 46% of the time.

Answer

There is a 95% probability that the true proportion is exactly 0.40.