Inference Statistics

A college recruiter is interested in comparing the SAT math and verbal scores of applicants to the college. An SRS of 40 applicants is chosen, and the math and verbal scores are noted. Which of the following is a proper test?

• Test of difference in two population means.

• Test of difference in two population proportions.

• One sample test on differences of paired data.

• Chi-square goodness-of-fit test.

• Chi-sqaured test for homogeneity.

Two confidence interval estimates from the same sample size are (72.2, 77.8) and (71.3, 78.7). One estimate is at the 95 percent level, and the other is at the 99 percent level. Which is which?

• (72.2, 77.8) is the 95 percent level.

• (72.2, 77.8) is the 99 percent level.

• This question cannot be answered without knowing the sample size.

• This question cannot be answered without knowing the sample standard deviation.

• This question cannot be answered without knowing both the sample size and standard deviation.

A researcher believes that a new diet should improve weight gain in laboratory mice. If the average gain for 12 mice on the new diet is 5.3 ounces with a standard deviation of 0.5 ounces, while 15 control mice on the old diet gain an average of 5 ounces with a standard deviation of 0.4 ounces, where is the P-value?

• Below .01

• Between .01 and .025

• Between .025 and .05

• Between .05 and .10

• Over .10

Which of the following would result in the widest confidence interval?

• Small sample size and 95 percent confidence

• Small sample size and 99 percent confidence

• Large sample size and 95 percent confidence

• Large sample size and 99 percent confidence

• This cannot be answered without knowing an appropriate standard deviation.

A fitness center advertises that the average pulse rate of its members is 68.4 bpm. A high school AP Statistics instructor suspects this is a made-up number and runs a hypothesis test on an SRS of 48 members, calculating a mean of 71.0 bpm with a standard deviation of 10.3 bpm. In which of the following intervals is the P-value located?

• P < .01

• .01 < P < .02

• .02 < P < .05

• .05 < P < .10

• P > .10

A government statistician claims that the mean income level of families living in subsidized housing is $9.250 with a standard deviation of $2,575. A reporter plans to test this claim through interviews with a random sample of 50 families. If she finds a sample mean more than $500 different from the claimed $9,250, she will dispute the statistician's claim. What is the probability that the reporter will mistakenly reject a true claim?

• .043

• .085

• .170

• .830

• .915

A high school has six math teachers and six science teachers. When comparing their mean years of service, which of the following is most appropriate?

• A two-sample z-test of population means

• A two-sample t-test of population means

• A one-sample z-test on a set of differences

• A one-sample z-test on a set of differences

• None of the above are appropriate.

Which of the following are true statements?

I. A P-value is a conditional probability.

II. The P-value is the probability that the null hypothesis is true.

III. A P-value is the probability that the null hypothesis is true given a particular observed statistic.

• I only

• II only

• III only

• I and II

• I and III

The school superintendent wants to know what percentage of property owners are willing to support an increase in school taxes. What sample size should be obtained to determine with 90 percent confidence the support level to within 5 percent?

• 17

• 33

• 271

• 289

• 1,083

In general, how does doubling the sample size change the confidence interval size?

• Doubles the interval size

• Halves the interval size

• Multiplies the interval size by 1.414

• Divides the interval size by 1.414

• This question cannot be answered without knowing the sample size.