Midterm2Practice-SP22-KEY

ST 312: Midterm 2 Review Problems Part I: Multiple Choice, True/False Questions 1. When is the Satterthwaite approximation for the degrees of freedom necessary? a. When the population variances are unknown b. When the population variances are unequal c. When the population variances are equal d. When the data are paired e. When the sample variances are unequal 2. A pooled variance estimator is used when… a. The data is paired b. Calculating the sample size c. The null hypothesis is true d. The variances of two populations are assumed equal e. The variances of two populations are unequal 3. A pooled proportion estimator is used when… a. The sample proportions are unknown b. Finding the minimum sample size c. Conducting a hypothesis test for ? 1 − ? 2 d. Constructing a confidence interval for ? 1 − ? 2 e. All of the above 4. The Normal distribution can be used as the sampling distribution under the null hypothesis for a test concerning ? 1 − ? 2 if… a. The sample sizes ( 𝑛 1 , 𝑛 2 ) are larger than 30 b. The distributions of 𝑋 1 and 𝑋 2 are binomial c. Either 𝑛 1 ? 1 , 𝑛 1 ? 1 ≥ 10 or 𝑛 2 ? 2 , 𝑛 2 ? 2 ≥ 10 d. Both 𝑛 1 ? 1 , 𝑛 1 ? 1 ≥ 10 and 𝑛 2 ? 2 , 𝑛 2 ? 2 ≥ 10 5. The Normal distribution can be used as the sampling distribution under the null hypothesis for a test concerning 𝜇 1 − 𝜇 2 if… a. The sample sizes ( 𝑛 1 , 𝑛 2 ) are larger than 30 b. The distributions of 𝑋 1 and 𝑋 2 are Normal c. The variances ( 𝜎 1 , 𝜎 2 ) are known d. Both a and c above e. Either a or b , and c above

6. A Chi- Square statistic can be used to test for independence when… a. The sample size is at least 30 b. The observed cell counts are all 5 or greater c. The expected cell counts are all 5 or greater d. The test statistic is larger than the critical value 7. A hypothesis test to determine if the mean of population A is larger than the mean of population B finds a test statistic of 1.85. Interpret this value. a. The difference between 𝜇 ? and 𝜇 ? is 1.85. b. The difference between 𝑥̅ ? and 𝑥̅ ? is 1.85. c. If the population means were equal, the difference between 𝑥̅ ? and 𝑥̅ ? lies 1.85 standard deviations above 0. d. If the population means are both 0, the difference between 𝑥̅ ? and 𝑥̅ ? lies 1.85 standard deviations above 0. 8. A hypothesis test to determine if the mean difference of treatment A and treatment B is greater than 0 results in a p-value of 0.04. Interpret this value. a. The probability that the null hypothesis is true is 0.04. b. The probability that the mean difference is greater than 0 is 0.04. c. The probability of observing a mean difference equal to or greater than the sample mean difference is equal to 0.04. d. The probability of observing a mean difference equal to or greater than the sample mean difference, assuming the true mean difference is 0, is equal to 0.04. e. The probability of observing a mean difference equal to or greater than 0, assuming the true mean difference is greater than or equal to than the sample mean difference, is equal to 0.04. 9. The t critical value for a 95% confidence interval estimation with 24 degrees of freedom is a. 1.71 b. 2.064 c. 2.492 d. 2.069 10. The z critical value for a 99% confidence interval estimation is a. 1.645 b. 1.96 c. 2.33 d. 2.58

11. The rejection region for a Chi-square test of independence where 𝛼 = 0.05 and the two-way table consists of 4 rows and 3 columns is a. ?? = {𝜒 2∗ < 11.07} b. ?? = { 𝜒 2 ∗ > 12 .59 } c. ?? = {𝜒 2∗ < 12.59} d. ?? = {𝜒 2∗ > 14.07} e. ?? = {𝜒 2∗ > 21.03} f. ?? = {𝜒 2∗ < 21.03} 12. In a two-tailed hypothesis test the test statistic z* is determined to be -2.5. The p-value for this test is a. -1.25 b. 0.4938 c. 0.0062 d. 0.0124 13. In a left-tailed hypothesis test, the test statistic z* is determined to be -2. The p-value for this test is a. 0.4772 b. 0.0228 c. 0.0056 d. 0.0238 14. In a left-tailed hypothesis test, the test statistic t* is determined to be -2 with df = 9. The p-value for this test is a. 0.038 b. 0.962 c. 0.000 d. 1.0 15. A test for paired differences uses which sampling distribution? a. A standard normal b. A t distribution with df = the total number of observations c. A t distribution with df = the total number of observations - 1 d. A t distribution with df = the total number of differences e. A t distribution with df = the total number of differences – 1

16. The value added and subtracted from a point estimate in order to develop an interval estimate of the population parameter is known as the a. confidence level b. margin of error c. confidence coefficient d. parameter estimate e. interval estimate f. critical value 17. Which value(s) are used as an estimator(s) for the proportions ? 1 and ? 2 when calculating the standard error of ?̂ 1 − ?̂ 2 during a hypothesis test? a. ?̂ 1 b. ?̂ 2 c. Both ?̂ 1 and ?̂ 2 d. ?̂ 18. If a test rejects 𝐻 0 : µ 1 = µ 2 , then the confidence interval for (μ 1 – μ 2 ) having the same error rate does not contain zero. a. True b. False 19. If the calculated value of the t test statistic is negative, then there is strong evidence that the null hypothesis is false. a. True b. False 20. Expected cell counts are calculated the same way in the tests for independence and goodness- of-fit. a. True b. False 21. The Chi-square goodness-of-fit test always assumes the proportions to be equal under the null hypothesis. a. True b. False 22. A Chi-square test for independence returns a test statistic that is greater than the critical value. We can conclude that the variables are dependent. a. True b. False