2/3 Examination: Sample Questions and Answers

Sample Questions for 2/3 Exam from Previous Years Click on the "answer" term below for the answer and explanation.   Which test statistic --- (1) z-score, (2) t-score, (3) F ratio ---- would be most suitable for testing relationships between these pairs of variables?   1.______ Difference in mens' and womens' attendance rates at religious services   2.______ Difference in the predicted mean Republican vote in 1998 by the Gallup poll with 900 interviews and the CBS poll with 1,200.   3.______ Literacy rates by countries and a classification of countries by region. Answers for all three   4. The formula provides an unbiased estimate of the population: 1- standard deviation 2- standard error 3- sum of squares 4- variance Answer 5. The standard error of the mean is 1- an unbiased estimate of the population mean 2- equal to the standard deviation of the sample data 3- the standard deviation of the sampling distribution of means 4- the descriptive statistic that measures dispersion Answer 6. The standard error of the mean is equal to Answer 7. Given a sample size of 100, mean of 36, population standard deviation of 5, and confidence level of .95, the confidence interval for the mean of the population is closest to 1- 31 to 41 2- 26 to 46 3- 35.5 to 36.5 4- 35 to 37 Answer 8. In practical terms, the amount of accuracy in predicting from national samples to the U.S. Population is least dependent on 1- the proportion that the sample is of the population 2- the absolute number of cases in the sample 3- the population variance for the attribute being estimated 4- the procedure used in drawing the sample Answer 9. Which of the following terms does not belong with the other terms? 1- Type I error 2- alpha level 3- region of rejection 4- z-score Answer 10. Which of the following statistical distributions is interpreted with reference to two different degrees of freedom? 1- F 2- t 3- skewed 4- normal Answer 11. If one has a directional hypothesis, he or she especially wants to 1- make a one-tailed test 2- make a two-tailed test 3- guard against a Type I error 4- guard against a Type II error Answer 12. The sampling distribution of the difference between two means for independent samples -- 1- is unknown and therefore one cannot test differences between two means against a null hypothesis. 2- is not subject to the Central Limit Theorem. 3- has a standard error equal to the difference in the standard errors of the individual samples. 4- tends to become normal as the sample sizes increase. Answer 13. In the analysis of variance model, the null hypothesis of no difference among the means for the subgroups will tend to be rejected as 1- the "between group" variance exceeds the "within group" variance. 2- the "within group" variance begins to exceed the "between group" variance. 3- the "within" and "between" group variance approach equality. 4- both the "between" and the "within" group variance approach total variance. Answer   14. Which statement is true about data expressed in proportions? 1- You cannot treat proportions as interval data. 2- You cannot compute variance for a dichotomized variable expressed as proportions. 3- Proportions computed for a dichotomized variable are simply a type of mean. 4- Transforming percentage data into proportions is an example of a nonlinear transformation. Answer 15. Another name for "between groups" sum of squares in the analysis of variance is 1- unexplained variation 2- deviations about the regression line 3- explained variation 4- error variance Answer 16. An unbiased estimator of a population parameter is 1- a statistic whose mean value of its own sampling distribution is equal to the population parameter. 2- a statistic with a relatively small sampling error. 3- a statistic that predicts to the population with a known bias. 4- impossible to calculate if the population lacks a normal distribution. Answer 17. Calculate the variance for this set of numbers: -5,-5,-5,5,5,5 Variance = _____ Answer 18. According to the table of areas under the normal curve, what positive and negative z-score value would be used to establish the region of rejection for a TWO-tailed test nearest to the .04 level of significance? z-score = __________ Answer   Here is T-TEST output comparing Democrat and Republican Members of Congress, with the dependent variable being a scale of increasing"conservatism" in voting on social issues. Answer questions 19 and 20. VARIABLE NUMBER STANDARD STANDARD OF CASES MEAN DEVIATION ERROR DEMOCRATS 248 30.5806 23.441 1.488 REPUBLICANS 180 65.7278 16.318 1.216 Mean Difference = -35.1472 Levene's Test for Equality of Variances:F= 2.06 P= .000 Variances t-value df 2-TailSig Equal -17.30 426 .000 Unequal -18.28 425.31 .000 19.Which expression below was used to compute the degrees of freedom for Equal Variance estimate of the T-Test above? 1- (N - 1) 2- (k - 1) 3- (N - 2) 4- (N1 + N2 - 2) Answer   20. Which statement about the above T-TEST output is true? 1- It shows that DEMOCRATS were actually more conservative on social issues than Republicans 2- It shows that REPUBLICANS showed much more variation in voting on conservative issues than DEMOCRATS. 3- The F-value is significant at the .05 level, indicating that the population variance are equal and that you are advised to use the Unequal variance estimate rather than the Equal estimate in checking the significance of t. 4- Regardless of which estimate you use, the T-TEST shows that both groups of Representatives do NOT differ significantly in voting on social issues, so the null hypothesis CANNOT be rejected. Answer   Below is SPSSx output from MEANS for GNP PER CAPITA in the POLITY data analyzed by type of government. Answer questions 21, 22, 23, and 24 with reference to this output.   DEPENDENT VARIABLE GNPPCA80 GNP PER CAPITA IN US DOLLARS-1980 INDEPENDENT VARIABLE POLTYPE TYPE OF POLITICAL SYSTEM VARIABLE VALUE LABEL MEAN STD DEV CASES FOR ENTIRE POPULATION 3633.0864 4267.0914 81 POLTYPE 1.00 PARLIAMENT/DEMOCRACY 6511.4815 4608.2098 27 POLTYPE 2.00 DEMOCRATIC & FEDERAL 9598.0000 5869.8825 5 POLTYPE 3.00 MULTIPARTY DEMOCRACY 1322.8571 1334.9746 7 POLTYPE 4.00 DEMOCRATIC FORM 2210.0000 113.1371 2 POLTYPE 5.00 MILITARY GOVERNMENT 895.8333 900.6408 12 POLTYPE 8.00 ONEPARTY COMMUNIST 3587.5000 2431.3180 8 POLTYPE 9.00 ONEPARTY SOCIALIST 2270.0000 494.9747 2 POLTYPE 10.00 ONEPARTY MARXIST 276.6667 140.1190 3 POLTYPE 11.00 ONEPARTY STATE 798.6667 1015.8168 15 SUM OF MEAN SOURCE SQUARES D.F. SQUARE F SIG. BETWEEN GROUPS 690959683.13 8 WITHIN GROUPS 765685845.26 72 21. Showing the math, compute the MEAN SQUARE for BETWEEN GROUPS to one decimal: _____________ Answer   22. Showing the math, compute the F ratio to one decimal: _____________ Answer     23. Which statement gives the most accurate assessment of that relationship? 1- The null hypothesis can be rejected at the .10 level. 2- The null hypothesis can be rejected at the .05 level. 3- The null hypothesis can be rejected at the .01 level. 4- The observed differences in GNP by government type can occur about 20 times out of 100 on the basis of chance alone. Answer 24. Under the null hypothesis, the expected value of Pearson's r is 1- dependent on sample size 2- not used in two-tailed tests 3- unknown unless the t value is computed 4- zero Answer   25. What condition exists when the variance of Y remains the same for different values of X? 1- homoscedasticity 2- unbiasedness 3- normality 4- linearity Answer   26. This formula for testing the significance of r: , assumes that 1- the F table is used to determine level of significance. 2- that you have no degrees of freedom in computing the significance. 3- there is no difference between the observed and expected correlation. 4- the test is against the null hypothesis that the population correlation, r (rho), is equal to 0. Answer 27. If data for 2 variables are transformed into z-scores and then correlated, [This topic was not covered.] 1- the product moment correlation will be equal to the beta coefficient in the associated regression equation. 2- the beta coefficient will be equal to the b-coefficient in the regression equation. 3- the intercept in the regression equation will be equal to 0. 4- all of the above are true. Answer   28.Tested against the null hypothesis, a highly significant correlation merely indicates that 1- it is unlikely that there is no relationship between the variables in the universe. 2- knowledge of one variable will substantially improve prediction of the value of an observation on the other variable. 3- there is a strong relationship between the variables in the universe. 4- there is a strong relationship between the variables in the sample. Answer 29. Which statistic is most appropriate for testing the significance of the difference among means for four independent samples? 1- t-test 2- beta coefficient 3- F ratio 4- b coefficient Answer   30. The condition of heteroscedasticity is best shown in which diagram? Answer