Take this Quiz: AP Statistics — statistical inference | Zestly

Question 1

A researcher at the invented Zenith Institute reports a ninety-five per cent confidence interval for the mean height of a plant species. Which statement interprets that interval correctly?

Accepted Answer

If the whole sampling procedure were repeated many times, about ninety-five per cent of the intervals it produced would contain the true mean height

Answer

Ninety-five per cent of the plants in the population have heights lying inside this interval

Answer

Ninety-five per cent of all possible sample means drawn from this population would lie inside this particular interval

Answer

There is a ninety-five per cent probability that the true mean height lies inside this particular interval

Question 2

A team at the invented firm Apex Analytics wants a narrower confidence interval for a population proportion, while keeping the confidence level at ninety-five per cent. Which change achieves that?

Accepted Answer

Survey a larger sample, drawn in the same way

Answer

Raise the confidence level to ninety-nine per cent, since greater confidence means a more precise estimate

Answer

Report the endpoints of the interval to more decimal places

Answer

Draw a second sample of the same size and report whichever of the two intervals turns out to be narrower

Question 3

A scientist at the invented Nova Research Group is testing whether the mean weight of a new polymer exceeds fifty grams. Which set of hypotheses is correctly stated?

Accepted Answer

$H_0: \mu = 50$; $H_a: \mu > 50$

Answer

$H_0: \bar{x} > 50$; $H_a: \bar{x} = 50$

Answer

$H_0: \bar{x} = 50$; $H_a: \bar{x} > 50$

Answer

$H_0: \mu > 50$; $H_a: \mu = 50$

Question 4

In an invented study at Echo Labs a researcher obtains a p-value of 0.03 while testing a null hypothesis. What does that number mean?

Answer

The probability that the null hypothesis is true is 0.03

Answer

The probability that the alternative hypothesis is true is 0.97

Answer

The probability that the observed result arose purely by chance is 0.03

Answer

If the null hypothesis were true, a result at least as extreme as the one observed would arise about three times in a hundred

Question 5

A researcher at the imaginary Solstice Institute performs a hypothesis test with a significance level of $\alpha = 0.05$ and obtains a p-value of 0.08. Which conclusion is appropriate?

Answer

Reject the null hypothesis because the result is statistically significant.

Answer

Accept the null hypothesis as true because the p-value is greater than $\alpha$.

Answer

Fail to reject the null hypothesis because there is insufficient evidence to conclude the alternative is true.

Answer

Conclude that the null hypothesis is false but the effect is not large enough to be important.