EXAM III Research Methods and Statistics PSY 418 Instructor: Bob Josephs Exam III KEY1. The null hypothesis for the independent-measures t-test states ______. a. µ1 - µ2 = 0 b. µD = 0 c. M1 - M2 = 0 d. µ = 0 2. One sample of n = 5 scores has a variance of s2 = 10 and a second sample of n = 10 scores has a variance of s2 = 20. If the pooled variance is computed for these two samples, then the value obtained will be: a. closer to 20 than to 10. b. closer to 10 than to 20. c. exactly halfway between 10 and 20. d. cannot be determined without more information. 3. For a repeated-measures hypothesis test, the null hypothesis states ______. a. MD = 0 b. µD = 0 c. µ1 = µ2 d. M1 = M2 4. An independent-measures research study uses two samples, each with n = 16 participants. If the data produce a t = 2.10, then which of the following is the correct decision for a two-tailed hypothesis test? a. Reject the null hypothesis with a = .05 but fail to reject with a = .01. b. Reject the null hypothesis with either a = .05 or a = .01. c. Fail to reject the null hypothesis with either a = .05 or a = .01. d. Cannot answer without additional information. 5. A researcher uses a repeated-measures study to compare two treatment conditions with a set of 20 scores in each treatment. What would be the value of df for the repeated measures t statistic? a. df = 19 b. df = 18 c. df = 39 d. df = 38 6. If the null hypothesis is true, what value is expected on average for the related-samples t statistic? a. 0 b. 1 c. 1.96 d. t > 1.967. Assuming that other factors are held constant, which of the following would tend to decrease the value of the calculated t statistic? a. Increase the sample size. b. Increase the sample mean difference. c. Increase the sample variance. d. None of these would produce a decrease in the value of t. 8. The purpose of a confidence interval is to ______. a. use a level of confidence to estimate a sample mean. b. use the sample mean to determine a level of confidence. c. use a population mean or mean difference to predict a sample mean or mean difference. d. use a sample mean or mean difference to estimate the corresponding population mean or mean difference. 9. What value(s) for t would be used for a point estimate of a population mean using a single-sample t statistic? a. cannot answer without additional information b. t = ±1.00 c. t = 0 d. t = ±1.96 10. Assuming that all other factors are held constant, which confidence level will produce the smallest width for a confidence interval? a. 75% b. 99% c. 60% d. 90% 11. The 95% confidence interval for µ is computed from sample data and the interval estimate ranges from 115 to 125. This indicates that ______. a. 95% of the scores in the population fall between X = 115 and X = 125. b. you should reject H0 for any sample value between 115 and 125. c. the standard error is 10. d. you can be 95% confident that this interval contains the population mean. 12. An independent-measures study with a total of 16 participants is used to construct a 99% confidence interval for the population mean difference between two treatment conditions. The correct t values for the interval are _________. a. ±2.624 b. ±2.602 c. ±2.947 d. ±2.97713. A researcher reports an F-ratio with df = 1, 24 for an independent-measures experiment. How many individual subjects participated in the experiment? a. N = 26 b. N = 24 c. N = 25 d. N = 27 14. If the null hypothesis is true and there is no treatment effect, what value is expected on average for the F-ratio? a. k-1 b. 0 c. N-k d. 1.00 15. An independent-measures experiment uses one sample with n=6 and a second sample with n=10 to compare two experimental treatments. The t statistic from this experiment will have degrees of freedom equal to: a. 7 b. 14 c. 15 d. 8 16. A researcher conducts an experiment comparing three treatment conditions with a separate sample of n=8 in each treatment. An analysis of variance is used to evaluate the data, and the results of the ANOVA are presented in the table below. Fill in all missing values in the table. Source SS df MS F Between Treatments 12 _______ _______ F = 2.00 Within Treatments _______ _______ _______ XXXXXX Total _______ _______ XXXXXX XXXXXX 16. ANS: Source ! ! SS df MS Between Treatments 12 2 6 F = 2.00 Within Treatments 63 21 3 Total 75 23 17. In the above analysis of variance, use α = .05 to determine whether or not there is any evidence of any significant differences among the three treatments. Show the critical value of F, state whether you reject or fail to reject the null hypothesis, and explain what it means.17. ANS: With df=2,21, the critical value is 3.47 (1 pt). Fail to reject H0 (1 pt) and conclude that there are no significant differences among the three treatments. 18. City dwellers and suburbanites (N=150) were surveyed about a budget proposal that would allocate extra funding toward the renovation of city parks. The frequencies from this survey are shown in the first table below. Use the second table below to fill in the cell values that would result if Ho is true—that opinion is independent of home location. Observed Frequencies: Opinion Favor Oppose City 35 15 Suburb 55 45 If Ho is true: Opinion Favor Oppose City 30 20 Suburb 60