AP Statistics Inference Tests and Intervals

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 Ha: 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, Ha: p < 0.486 would be more appropriate.

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

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

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

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.

To test whether husbands or wives have greater manual agility, an SRS of 50 married couples is chosen, and all 100 people are given a 1-minute period to find a place strangely shaped pegs into matching holes. What is the conclusion at a 5% significance level if a two-sample hypothesis test: H₀: u₁ - u₂ = 0, H_a: u₁ - u₂ ≠ 0, results in a p-value of 0.15

• The observed difference between husbands and wives is significant.

• The observed difference is not significant.

• A conclusion is not possible without knowing the mean number of pegs placed by husbands and wives.

• A conclusion is not possible without knowing both the mean and standard deviation of the number of pegs placed by husbands and by wives.

• A two-sample hypothesis test should not be used in this example.

I20: An office manager believes that the percentage of employees arriving late is even greater than the previously claimed 7%. She conducts a hypothesis test on a random 200 employee arrivals and finds 23 punching in late. Is this strong evidence against the 0.07 claim?

• Yes, p-value is 0.0062

• Yes, p-value is 2.5

• No, p-value is only 0.0062

• No, p-value is over 0.10

• There is insufficient information to reach a conclusion.

When making an inference about a population mean, which of the following suggests the use of z-scores rather than t-scores?

• Outliers are absent.

• The population is normal.

• The sample size is under 30.

• Strong skew is absent.

• The population standard deviation is known.

A congressional representative serving on the Joint Committee on Taxation states that the average yearly charitable contributions for taxpayers is $1,250. A lobbyist for a national church organization who believes that the real figure is lower samples 12 families and comes up with a mean of $1,092 and a standard deviation of $308. Where is the p-value?

• Below 0.01

• Between 0.01 and 0.025

• Between 0.025 and 0.05

• Between 0.05 and 0.10

• Over 0.10