AP Statistics Quiz Bowl - Inference Part 1

I1: In a random sample of 1,250 adult drivers, 450 said that they would cut their driving by 10% if this significantly helped the environment. Which of the following would be the standard error for a 95% confidence interval?

• 0.00102

• 0.00849

• 0.00255

• 0.01358

• 0.00038

I2: A guidance counselor is interested in comparing GPAs of students with home access to the Internet with students who do not have this access. She pulls the files of an SRS of ten students who do have home access to the Internet and an SRS of ten who do not, and proceeds to run a t-test to compare the mean GPAs of each group. Which of the following is a necessary assumption?

• The population standard deviations from each group are known.

• The population standard deviations from each group are unknown.

• The population standard deviations from each group are equal.

• The population of GPA scores from each group is normally distributed.

• The samples must be independent samples, and for each sample np and n(1-p) must both be at least 10.

I6: A 2007 survey of 980 American drivers concluded that 38% of the driving population would be willing to pay higher gas prices to protect the environment. Which of the following best describes what is meant by the poll having a margin of error of 3%?

• 3% of those surveyed refused to participate in the poll.

• It would be be unexpected for 3% of the population to readily agree to the higher gas prices.

• Between 343 and 402 of the 980 drivers surveyed responded that they would be willing to pay higher gas prices to protect the environment.

• If a similar survey of 980 American drivers was taken weekly, a 3% change in each week's results would not be unexpected.

• It is likely that between 35% and 41% of the driving population would be willing to pay higher gas prices to protect the environment.

I8: A survey of 1,000 Americans reveals that 525 believe that whales are an endangered animal and should have protection from the fishing industry. In a survey of 750 Japanese, 325 believe that whales are endangered and should be protected. To test at the 5% significance level whether or not the data are significant evidence that the proportion of Japanese who believe that whales need protection is less than the proportion of Americans with this believe, a students sets up the following: H₀: p = 0.525 and H_a: p < 0.525, where p is the proportion of Japanese with this belief. Which of the following is a true statement?

• The student has set up a correct hypothesis test.

• Given the large sample sizes, a 1 percent significance level would be more appropriate.

• A two-sided test would be more appropriate.

• Given the pooled proportion is 0.486, H_a: p < 0.486 would be more appropriate.

• A two-population difference in proportions hypothesis test would be more appropriate.

I10: A fitness center advertises that the average pulse rate of its members is 68.4 bpm. A high school AP Stats 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 < 0.01

• 0.01 < p < 0.02

• 0.02 < p < 0.05

• 0.05 < p < 0.10

• p > 0.10

I11: A guidance counselor wishes to determine the mean number of changes in academic major by college students to within ± 0.1 at a 90% confidence level. What sample size should be chosen if it is known that the standard deviation is 0.45?

• 8

• 54

• 55

• 78

• 110

I12: In a one-sided hypothesis test for the mean, for a random sample of size 15 the t-score of the sample mean is 2.615. Is this significant at the 5% level? At the 1% level?

• Significant at 1%, not at 5%

• Significant at 5%, not at 1%

• Significant at both

• Significant at neither

• There is not enough information to determine

I13: A confidence interval estimate is determined from the summer earnings of an SRS of n students. All other things being equal, which of the following will result in a smaller margin of error?

• A greater confidence level

• A larger sample standard deviation

• A larger sample size

• Accepting less precision

• Introducing bias into sampling

I14: Which of the following is a true statement?

• Tests of significance (hypothesis tests) are designed to measure the strength of evidence against the null hypothesis.

• A well-planned test of significance should result in a statement either that the null hypothesis is true or that it is false.

• The null hypothesis is one-sided and expressed using either < or > if there is interest in deviations in only one direction.

• When a true parameter value is farther from the hypothesized value, it becomes easier to reject the alternative hypothesis.

• Increasing the sample size makes it more difficult to conclude that an observed difference between observed and hypothesized values is significant.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.5

I16: Two confidence interval estimates from the same sample are (72.2, 77.8) and (71.3, 78.7). One estimate is at the 95% level and the other is at the 99% level. Which is which?

• (72.2, 77.8) is the 95%

• (72.2, 77.8) is the 99%

• 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.

Tags

CCSS.HSS.ID.A.4