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Inference for Means and Proportions Multiple Choice Practice Problems for AP Statistics

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By — McGraw-Hill Professional
Updated on Apr 25, 2014

Review the following concepts if necessary:

Problems

Assuming that the speeds are approximately normally distributed, how many degrees of freedom will there be in the appropriate t-test used to determine which type of tennis ball travels faster?

  1. A school district claims that the average teacher in the district earns $48,000 per year. The teachers' organization argues that the average salary is less. A random sample of 25 teachers yields a mean salary of $47,500 with a sample standard deviation of $2000. Assuming that the distribution of all teachers' salaries is approximately normally distributed, what is the value of the t-test statistic and the P-value for a test of the hypothesis H0: μ = 48,000 against HA: μ < 48,000?
    1. t = 1.25, 0.10 < P < 0.15
    2. t = –1.25, 0.20 < P < 0.30
    3. t = 1.25, 0.20 < P < 0.30
    4. t = –1.25, 0.10 < P < 0.15
    5. t = –1.25, P > 0.25
  2. Which of the following conditions is (are) necessary to justify the use of z-procedures in a significance test about a population proportion?
    1. The samples must be drawn from a normal population.
    2. The population must be much larger (10–20 times) than the sample.
    3. np0 ≥ 5 and n(1 – p0) ≥ 5.
    1. I only
    2. I and II only
    3. II and III only
    4. III only
    5. I, II, and III
  3. A minister claims that more than 70% of the adult population attends a religious service at least once a month. Let p = the proportion of adults who attend church. The null and alternative hypotheses you would use to test this claim would be:
    1. H0: p ≤ 0.7, HA: p > 0.7
    2. H0: μ ≤ 0.7, HA: μ > 0.7
    3. H0: p = 0.7, HA: p ≠ 0.7
    4. H0: p ≤ 0.7, HA: p < 0.7
    5. H0: p ≥ 0.7, HA: p < 0.7
  4. A t-test for the difference between two populations means is to be conducted. The samples, of sizes 12 and 15, are considered to be random samples from independent, approximately normally distributed, populations. Which of the following statements is (are) true?
    1. If we can assume the population variances are equal, the number of degrees of freedom is 25.
    2. An appropriate conservative estimate of the number of degrees of freedom is 11.
    3. The P-value for the test statistic in this situation will be larger for 11 degrees of freedom than for 25 degrees of freedom.
    1. I only
    2. II only
    3. III only
    4. I and II only
    5. I, II, and III
  5. When is it OK to use a confidence interval instead of computing a P-value in a hypothesis test?
    1. In any significance test
    2. In any hypothesis test with a two-sided alternative hypothesis
    3. Only when the hypothesized value of the parameter is not in the confidence interval
    4. Only when you are conducting a hypothesis test with a one-sided alternative
    5. Only when doing a test for a single population mean or a single population proportion
  6. Which of the following is not a required step for a significance test?
    1. State null and alternative hypotheses in the context of the problem.
    2. Identify the test to be used and justify the conditions for using it.
    3. State the significance level for which you will decide to reject the null hypothesis.
    4. Compute the value of the test statistic and the P-value.
    5. State a correct conclusion in the context of the problem.
  7. Which of the following best describes what we mean when say that t-procedures are robust?
    1. The t-procedures work well with almost any distribution.
    2. The numerical value of t is not affected by outliers.
    3. The t-procedures will still work reasonably well even if the assumption of normality is violated.
    4. t-procedures can be used as long as the sample size is at least 40.
    5. t-procedures are as accurate as z-procedures.
  8. For a hypothesis test of H0 : μ = μ0 against the alternative HA : μ < μ0, the z-test statistic is found to be 2.00. This finding is
    1. significant at the 0.05 level but not at the 0.0l level.
    2. significant at the 0.01 level but not at the 0.05 level.
    3. significant at both the 0.01 and the 0.05 levels.
    4. significant at neither the 0.01 nor the 0.05 levels.
    5. not large enough to be considered significant.
  9. Two types of tennis balls were tested to determine which one goes faster on a serve. Eight different players served one of each type of ball and the results were recorded:
    1. 6
    2. 7
    3. 16
    4. 15
    5. 14
  10. Two statistics teachers want to compare their teaching methods. They decide to give the same final exam and use the scores on the exam as a basis for comparison. They decide that the value of interest to them will be the proportion of students in each class who score above 80% on the final. One class has 32 students and one has 27 students. Which of the following would be the most appropriate test for this situation?
    1. Two proportion z-test
    2. Two-sample t-test
    3. Chi-square goodness-of-fit test
    4. One-sample z-test
    5. Chi-square test for independence
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