Take this Exam: AP Statistics — statistical inference | Zestly

Question 1

At the invented firm Titan Manufacturing a quality manager tests each batch against the claim that the proportion of defective components is no higher than the permitted level, and stops the production line when the evidence says otherwise. What is a Type I error here, and which error does the significance level control?

Accepted Answer

Stopping a line whose defect rate was in fact within the permitted level, and this is the error the significance level controls

Answer

Letting a line run whose defect rate was in fact too high, and this is the error the significance level controls

Answer

Stopping a line whose defect rate was in fact too high, which the significance level is chosen to make rare

Answer

Letting a line run whose defect rate was in fact within the permitted level, and the significance level controls how often this happens

Question 2

A team at the invented Horizon Research Centre wants to raise the power of a test they are planning. Which change would do it?

Accepted Answer

Enrol more subjects, so that the same true effect yields a larger test statistic

Answer

Lower the significance level from 0.05 to 0.01, so as to be surer of any effect that is found

Answer

Measure the outcome with a less precise instrument, so that the readings vary more widely

Answer

Set out to detect a smaller effect than was originally planned

Question 3

An invented study by the Global Data Group compares reaction times between two groups, with five million participants in all, and reports a difference significant at a p-value of 0.0001. Why should the researchers be cautious about what they claim?

Accepted Answer

Because a sample that large can make a difference of a few thousandths of a second statistically significant, and a difference that small may matter to nobody

Answer

Because a p-value that small usually points to a mistake in the calculation rather than to a real effect

Answer

Because the conditions for inference fail once a sample runs into the millions, so no test is valid at that size

Answer

No caution is needed, since a p-value of 0.0001 establishes that the difference is both real and large

Question 4

A researcher at the imaginary Vertex Lab wants to determine if there is an association between eye colour (blue, brown, green) and hair colour (blonde, brunette, black) in a group of two hundred people. Which test is most appropriate?

Answer

A two-sample t-test for means.

Answer

A one-sample z-test for a proportion.

Answer

A chi-square test for independence.

Answer

A matched-pairs t-test.

Question 5

A student at the invented Academy of Statistics gathers data by asking the first ten people she sees in the cafeteria about their study habits, then wants to build a confidence interval for the mean study time of all students at the college. Why is that inference unsound?

Answer

The student stated no null hypothesis before collecting the data, which every inference procedure requires

Answer

The data come from a convenience sample, so the random selection that every inference procedure assumes is missing

Answer

The sample of ten is simply too small, and asking fifty people in the same way would make the interval valid

Answer

No inference is possible without a controlled experiment, since only an experiment supports a conclusion about a population