Confidence Intervals and Introduction to Inference Multiple Choice Practice Problems for AP Statistics

Review the following concepts if necessary:

• Estimation and Confidence Intervals for AP Statistics
• Confidence Intervals for Means and Proportions for AP Statistics
• Sample Size for AP Statistics
• Statistical Significance and P-Value for AP Statistics
• The Hypothesis-Testing Procedure for AP Statistics
• Type-I and Type-II Errors and the Power of a Test for AP Statistics

Problems

1. You are going to create a 95% confidence interval for a population proportion and want the margin of error to be no more than 0.05. Historical data indicate that the population proportion has remained constant at about 0.7. What is the minimum size random sample you need to construct this interval?
   1. 385
   2. 322
   3. 274
   4. 275
   5. 323
2. Which of the following will increase the power of a test?
   1. Increase n.
   2. Increase α.
   3. Reduce the amount of variability in the sample.
   4. Consider an alternative hypothesis further from the null.
   5. All of these will increase the power of the test.
3. Under a null hypothesis, a sample value yields a P-value of 0.015. Which of the following statements is (are) true?
   1. This finding is statistically significant at the 0.05 level of significance.
   2. This finding is statistically significant at the 0.01 level of significance.
   3. The probability of getting a sample value as extreme as this one by chance alone if the null hypothesis is true is 0.015.
   1. I and III only
   2. I only
   3. III only
   4. II and III only
   5. I, II, and III
4. You are going to construct a 90% t confidence interval for a population mean based on a sample size of 16. What is the critical value of t (t*) you will use in constructing this interval?
   1. 1.341
   2. 1.753
   3. 1.746
   4. 2.131
   5. 1.337
5. A 95% confidence interval for the difference between two population proportions is found to be (0.07, 0.19). Which of the following statements is (are) true?
   1. It is unlikely that the two populations have the same proportions.
   2. We are 95% confident that the true difference between the population proportions is between 0.07 and 0.19.
   3. he probability is 0.95 that the true difference between the population proportions is between 0.07 and 0.19.
   1. I only
   2. II only
   3. I and II only
   4. I and III only
   5. II and III only
6. A 99% confidence interval for the true mean weight loss (in pounds) for people on the SkinnyQuick diet plan is found to be (1.3, 5.2). Which of the following is (are) correct?
   1. The probability is 0.99 that the mean weight loss is between 1.3 lbs and 5.2 lbs.
   2. The probability is 0.99 that intervals constructed by this process will capture the true population mean.
   3. We are 99% confident that the true mean weight loss for this program is between 1.3 lbs and 5.2 lbs.
   4. This interval provides evidence that the SkinnyQuick plan is effective in reducing the mean weight of people on the plan.
   1. I and II only
   2. II only
   3. II and III only
   4. II, III, and IV only
   5. All of these statements are correct.
7. In a test of the null hypothesis H₀ : p = 0.35 with α = 0.01, against the alternative hypothesis H_A : p < 0.35, a large random sample produced a z-score of –2.05. Based on this, which of the following conclusions can be drawn?
   1. It is likely that p = 0.35.
   2. p = 0.35 only 2% of the time.
   3. If the z-score were positive instead of negative, we would be able to reject the null hypothesis.
   4. We do not have sufficient evidence to claim that p < 0.35.
   5. 1% of the time we will reject the alternative hypothesis in error.
8. 8. A 99% confidence interval for the weights of a random sample high school wrestlers is reported as (125, 160). Which of the following statements about this interval is true?
   1. At least 99% of the weights of high school wrestlers are in the interval (125, 160).
   2. The probability is 0.99 that the true mean weight of high school wrestlers is in the interval (125, 160).
   3. 99% of all samples of this size will yield a confidence interval of (125,160).
   4. The procedure used to generate this confidence interval will capture the true mean weight of high school wrestlers 99% of the time.
   5. The probability is 0.99 that a randomly selected wrestler will weigh between 125 and 160 lbs.
9. This years' statistics class was small (only 15 students). This group averaged 74.5 on the final exam with a sample standard deviation of 3.2. Assuming that this group is a random sample of all students who have taken statistics and the scores in the final exam for all students are approximately normally distributed, which of the following is an approximate 96% confidence interval for the true population mean of all statistics students?
   1. 74.5 ± 7.245
   2. 74.5 ± 7.197
   3. 74.5 ± 1.871
   4. 74.5 ± 1.858
   5. 74.5 ± 1.772
10. A paint manufacturer advertises that one gallon of its paint will cover 400 sq ft of interior wall. Some local painters suspect the average coverage is considerably less and decide to conduct an experiment to find out. If m represents the true average number of square feet covered by the paint, which of the following are the correct null and alternative hypotheses to be tested?
    1. H₀ : μ = 400, H_A : μ > 400
    2. H₀ : μ ≥ 400, H_A : μ ≠ 400
    3. H₀ : μ = 400, H_A : μ ≠ 400
    4. H₀ : μ ≠ 400, H_A : μ < 400
    5. H₀ : μ ≥ 400, H_A : μ < 400