AP Statistics Significance Tests

In 1975, a random sample of 1484 adult U.S. citizens was surveyed, and 193 strongly agreed with the statement, "People should take care of themselves". Then, in 1991, a survey of 1013 adult U.S. citizens showed that only 61 strongly agreed with the statement. Does this indicate that the proportion of U.S.adults who strongly agree with the given statement has dropped?

• Two-Sample Z Test for the Difference in Proportions

• Two-Sample T Test for the Difference in Means

• Matched Pairs T Test for a Mean

• One-Sample T Test for a Mean

What is the Power of a test?

• A strong force

• The probability that we correctly reject a false null.

• The probability that we correctly accept a true null.

• How tough it is.

• The slope decreased and the r² increased.
• The slope increased and the r² decreased.
• The slope decreased but r² remained the same.
• Both slope and r² remained the same.

• A
• B
• C
• D

What happens to the shape of the t-distribution as the degrees of freedom increase?

• The middle of the distribution becomes shorter, while the tails get higher, approximating a more uniform model.

• The distribution becomes more and more similar to a normal distribution.

• Nothing. But the results of the hypothesis test become less accurate.

• The middle of the distribution becomes shorter, while the tails get taller, resulting in a bimodal model.

A wildlife biologist is doing research on chronic wasting disease and its impact on the deer populations in Colorado. To estimate the difference between the proportions of deer with chronic wasting disease in two different regions, a random sample of 200 deer was obtained from one region and a random sample of 197 deer was obtained from the other region. The biologist checked for the following (see pic). Which of the following conditions for inference was the biologist checking?

• The population of deer within each region is approximately normal.

• It is reasonable to generalize from the samples to the populations.

• The samples are independent of each other.

• The observations within each sample are close to independent.

• The sampling distribution of the difference in sample proportions is approximately normal.

A state political analyst wanted to see whether there is an association between the region where a person lives and whether the person is in favor of increasing the state gas tax. A random sample of 270 state residents was selected, and the table below shows the results of the survey. Which of the following is closest to the -value of the appropriate test to investigate whether there is an association between the region where a person lives and whether the person is in favor of increasing the state gas tax, and what is the correct decision?

• 0.0644, we reject the null hypothesis

• 0.3596, we reject the null hypothesis

• 0.0644, we fail to reject the null hypothesis

• 0.3596, we fail to reject the null hypothesis

What happens to the shape of the chi-square distribution as the degrees of freedom increase?

• Nothing.

• Eventually it will go from being right-skewed to normal.

• Eventually it will go from being right-skewed to left-skewed.

• It's peak will increase, becoming more right-skewed.

Given the regression analysis, what is the equation of the LSRL?

• y(hat)=38257x-0.163

• y(hat)=38257-0.163x

• y(hat)=2446-0.163x

• y(hat)=2446x-0.163

Researchers are testing a new diagnostic tool designed to identify a certain condition. The null hypothesis of the significance test is that the diagnostic tool is NOT effective in detecting the condition. For the researchers, the more consequential error would be that the diagnostic tool is not effective, but the significance test indicated that it is effective. Which of the following should the researchers do to avoid the more consequential error?

• Increase the significance level to increase the probability of Type I error

• Increase the significance level to decrease the probability of Type I error.

• Decrease the significance level to increase the probability of Type I error

• Decrease the significance level to decrease the probability of Type I error.