Download Multiple choice REVIEW QUESTIONS: Inference for mean difference.

 PRACTICE QUESTIONS FOR TWO-­‐SAMPLE TESTS ABOUT MEANS: 1. Which of the following refers to how the estimated difference between population means vary between different samples: a. Standard deviation of the sample b. Standard error of the sample c. Standard deviation of the mean d. Standard error of the difference 2. The purpose of ________ is to combine the variances of two samples into a single summary statistic a. s2 b. s 2pooled c.
sd2 d. d 3. Which of the following is TRUE for all of the 1-­‐sample and 2-­‐sample test statistics we have studied so far in this course? a. All dfs are computed in the same way. b. All are ratios of the “distance of the estimate from the null” to the variability of estimate. c. All use the same statistical table d. All use the same significance level to decide when the null hypothesis should be rejected 4. A study compared mean the hospital-­‐stay for heart transplant operations in 1999 to the mean stay in 1995. Two separate samples were collected in the two years. a. Since the same variable (“length of stay in the hospital”) is measured for both samples, the data should be analyzed using the one-­‐sample test for means. b. Since the same variable (“length of stay in the hospital”) is measured for both samples, the data should be analyzed using methods for dependent samples (such as the paired t test more mean difference). c. Since the same variable (“length of stay in the hospital”) is measured for both samples, the data should be analyzed using methods for independent samples (such as the two-­‐sample t-­‐test). d. None of the above. 5. Measurements on a random sample of babies born to mothers who took “Prescription Drug A” during pregnancy were compared to measurements on a random sample of babies born to mothers who did not take the drug. The difference in the mean head circumference between children born to the two groups of mothers had a P-­‐value = .03. Based only on this information you can conclude: a. There is a 3% chance the null hypothesis is true. b. Taking “Prescription Drug A” during pregnancy causes a reduction in child’s head circumference. c. Taking “Prescription Drug A” is associated with an increased child head circumference. d. The difference in child head circumference between the children whose mothers that took the drug, and those that did not, is larger than expected by chance. e. The sample mean difference in children’s head circumference between children born to the two groups of mothers is clinically important/significant. f. None of the above. 6. The average time in years to get an undergraduate degree in computer science was compared for men and women. Random samples of 100 male computer science majors and 100 female computer science majors were taken. Choose the appropriate parameter(s) for inference in this situation. a. One population proportion p. b. Difference between two population proportions p1 − p2. c. The true population mean μ1 d. Difference between two population means μ1 − μ2 7. The research question is whether the mean number of breeding horseshoe crabs in the Delaware Bay has gone up or down between 2011 and 2012. Horseshoe crabs breed on beeches, and the measurement variable is the number of breeding horseshoe crabs observed in 2011 and 2012. A random sample of 25 beaches was selected for a survey in 2011. In 2012, investigators returned to each beech for a re-­‐count; thus, each beach has one pair of measurements, one from 2011 and one from 2012. Choose the appropriate parameter(s) for inference in this situation. a. The true population mean μ for the Delaware Bay b. Difference between two means, μ1 − μ2, one for 2011 and one for 2012 c. The mean difference, μd, between beaches that were surveyed in both 2011 and 2012. d. Cannot be determined from the information given. 8. To compare the population mean annual incomes for residential (μ1) and out-­‐of-­‐province (μ2) construction workers, we constructed a 95% confidence interval for μ1 − μ2. Which of the following is statements is correct? a. If the confidence interval is (2000, 4000), then we can conclude that the spread of plausible values (at this confidence level) for the mean annual income ranges from $2000 to $4000 per year. b. If the confidence interval is (-­‐2000, 4000), then the corresponding hypothesis test of μ1 − μ2 = 0 against μ1 − μ2 ≠ 0 will have a P-­‐value > 0.05 c. If the confidence interval is (-­‐2000, 4000), then we can conclude that μ1 − μ2 = 0. d. If the confidence interval is (-­‐2000, 4000), then we can conclude that 95% of the residential workers in this province have annual income that range from $2000 less than, and $4000 more than the annual income of the out-­‐of-­‐province workers. 9. A random sample of 25 college males was obtained and each was asked to report their actual height and what they wished as their ideal height. A 95% confidence interval for μd = average difference between their ideal and actual heights was 0.8" to 2.2". Based on this interval, which one of the null hypotheses below (versus a two-­‐sided alternative) can be rejected? a. H0: μd = 0.5 b. H0: μd = 1.0 c. H0: μd = 1.5 d. H0: μd = 2.0 10. Measurements on babies of mothers who used marijuana during pregnancy were compared to measurements on babies of mothers who did not. The sample mean head circumference was larger in the group who were not exposed to marijuana. The 95% confidence interval for the difference in mean circumference between the 2 groups was .61 to 1.19 cm. What can be said about the (2-­‐sided) P-­‐value for testing the hypothesis of equal means? a. The P-­‐value is greater than 0.05 b. The P-­‐value is equal to 0.05 c. The P-­‐value is less than 0.05 d. The P-­‐value is 0 e. Cannot be determined from the information given. 11. Suppose a study reports a 90% confidence interval for μ1 − μ2 is (100, 300). Which one of the following statements is correct if you were to re-­‐compute the 90% confidence interval for μ2 – μ1? a. The confidence interval is (-­‐300,-­‐100). b. The confidence interval is (300, 100). c. The confidence interval is (100, 300). d. The confidence interval is (-­‐100, -­‐300). e. Cannot be determined from the information given. 12. True or False: When we do not reject H0 in a significance test, we are careful to say that “We do not reject H0” rather than “We accept H0” is because the null model assume a particular parameter value for H0, and the confidence interval tells us that value is just one of many plausible values for H0. a. True b. False Questions 13 to 21 below are based on the following study: A research study was conducted to examine the effect of Facebook on perceived life satisfaction. Ten subjects were selected who had never had a Facebook account and another ten subjects were randomly selected from a set of active Facebook users. All subjects were given a life satisfaction test known to have high reliability and validity. Scores on the measure range from 0 to 60 with high scores indicative of high life satisfaction; low scores indicative of low life satisfaction. The data are presented below. No Facebook Active Facebook 45 34 38 22 52 15 48 27 25 37 39 41 51 24 46 19 13. What is the null hypothesis for this study? a. H0: μd = 0 b. H0: μd > 0 c. H0: μ1 − μ2 = 0 d. H0: μ1 − μ2 > 0 e. H0: μd1 -­‐ μd2 = 0 f. H0: μd1 -­‐ μd2 > 0 14. What is the alternative hypothesis for this study? a. HA: μd = 0 b. HA: μd > 0 c. HA: μ1 − μ2 > 0 d. HA: μ1 − μ2 ≠ 0 e. H0: μd1 -­‐ μd2 = 0 f. H0: μd1 -­‐ μd2 > 0 15. What is the standard error of the difference between the mean life satisfaction scores of users and non-­‐users of Facebook? a. 3.85 b. 4.06 c. 8.61 d. 74.19 55 34 46 22 16. What is the value of the test statistic for this study? a. 0.22 b. 1.90 c. 4.03 d. 4.26 17. What are the degrees of freedom for this study? a. 20 b. 19 c. 18 d. 10 e. 9 f. 8 g. 2 18. What is the P-­‐value? a. P < 0.01 b. 0.05 < P < 0.01 c. 0.05 > P > 0.01 d. P > 0.01 19. Assuming a significance level of 0.05 for this study, what is your conclusion? a. Retain the Null hypothesis and claim that there is insufficient evidence for the claim that perceived life satisfaction differs between users and non-­‐users of Facebook. b. Reject the Null hypothesis and conclude that there is evidence that perceived life satisfaction differs between users and non-­‐users of Facebook. c. Reject the Null hypothesis and conclude that we have proved that the difference in perceived life satisfaction between users and non-­‐users of Facebook is greater than zero. d. Accept the Alternative hypothesis and conclude that the true difference in perceived life satisfaction between users and non-­‐users of Facebook is 16.4 on the life satisfaction test. 20. If you followed the rejection rule correctly and yet you made an error in this hypothesis test, what type of error would it be? a. Type I error b. Type II error c. None, if I correctly follow the rejection rule I will not make an error in a hypothesis test. 21. If we set the significance level of this test to 0.01, what would be the critical value for the t-­‐score? a. 2.878 b. 2.861 c. 2.845 d. 2.552 e. 2.539 f. 2.528 Questions 22 to 30 below are based on the following study: A researcher hypothesizes that electrical stimulation of the lateral habenula will result in a decrease in food intake (in this case, chocolate chips) in rats. Rats undergo stereotaxic surgery and an electrode is implanted in the right lateral habenula. Following a ten-­‐day recovery period, rats are tested for the number of chocolate chips consumed during a 10 minute period of time both with and without electrical stimulation. The data are presented below. Stimulation No stimulation 12 8 7 7 3 4 11 14 8 6 5 7 14 12 7 5 22. What is the null hypothesis for this study? a. H0: μd < 0 b. H0: μd = 0 c. H0: μd > 0 d. H0: μ1 − μ2 < 0 e. H0: μ1 − μ2 = 0 f. H0: μ1 − μ2 > 0 23. What is the alternative hypothesis for this study? a. HA: μd < 0 b. HA: μd = 0 c. HA: μd > 0 d. HA: μ1 − μ2 < 0 e. HA: μ1 − μ2 = 0 f. HA: μ1 − μ2 > 0 24. What is the standard error of the mean difference in food intake? a. 0.24 b. 0.76 c. 0.80 d. 2.40 9 5 10 8 25. What is the value of the test statistic for this study? a. 0.416 b. 1.0 c. 1.25 d. 1.31 26. What are the degrees of freedom for this study? a. 20 b. 19 c. 18 d. 10 e. 9 f. 8 g. 2 27. What is the P-­‐value? a. P < 0.10 b. P > 0.10 28. Assuming a significance level of 0.10 for this study, what is your conclusion? a. Retain the Null hypothesis and claim that you have proved that electrical stimulation of the lateral habenula will not result in a decrease in food intake in rats. b. Retain the Null hypothesis and conclude that there is insufficient evidence to support the claim that electrical stimulation of the lateral habenula will result in a decrease in food intake in rats. c. Reject the Null hypothesis and conclude that there is evidence that electrical stimulation of the lateral habenula will result in a decrease in food intake in rats. d. Accept the alternative hypothesis and conclude that we have proved that electrical stimulation of the lateral habenula will result in a decrease in food intake in rats. 29. If you followed the rejection rule correctly and yet you made an error in this hypothesis test, what type of error would it be? a. Type I error b. Type II error c. None, if I correctly follow the rejection rule I will not make an error in a hypothesis test. 30. If we set the significance level of this test to 0.01, what would be the critical value for the t-­‐score? a. -­‐3.355 b. -­‐3.250 c. -­‐3.169 d. -­‐2.896 e.
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Question: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 -­‐2.821 -­‐2.764 2.764 2.821 2.896 3.169 3.250 3.355 Answer: d b b c d d c b a c a a c d a d c a b a a b a b d e b b b e