答案和详解如下： Q1. We are examining the relationship between the number of cold calls a broker makes and the number of accounts the firm as a whole opens. We have determined that the correlation coefficient is equal to 0.70, based on a sample of 16 observations. Is the relationship statistically significant at a 10% level of significance, why or why not? The relationship is: A) significant; the t-statistic exceeds the critical value by 3.67. B) not significant; the critical value exceeds the t-statistic by 1.91. C) significant; the t-statistic exceeds the critical value by 1.91. Correct answer is C) The calculated test statistic is t-distributed with n – 2 degrees of freedom: t = r√(n – 2) / √(1 – r2) = 2.6192 / 0.7141 = 3.6678 From a table, the critical value = 1.76 Q2. A study of 40 men finds that their job satisfaction and marital satisfaction scores have a correlation coefficient of 0.52. At 5% level of significance, is the correlation coefficient significantly different from 0?
A) No, t = 1.68. B) Yes, t = 3.76. C) No, t = 2.02. Correct answer is B) H0: r = 0 vs. Ha: r ≠ 0 t = [r √(n – 2)] / √(1 – r2) < 0.522)="3.76" – √(1 √(38)] >="[(0.52"> tc (α = 0.05 and degrees of freedom = 38) = 2.021 t > tc hence we reject H0. Q3. Suppose the covariance between Y and X is 0.03 and that the variance of Y is 0.04 and the variance of X is 0.12. The sample size is 30. Using a 5% level of significance, which of the following is most accurate? The null hypothesis of: A) no correlation is rejected. B) significant correlation is rejected. C) no correlation is not rejected. Correct answer is A) The correlation coefficient is r = 0.03 / (√0.04 * √0.12) = 0.03 / (0.2000 * 0.3464) = 0.4330. The test statistic is t = (0.4330 × √28) / √(1 − 0.1875) = 2.2912 / 0.9014 = 2.54. The critical t-values are ± 2.048. Therefore, we reject the null hypothesis of no correlation. Q4. Consider a sample of 60 observations on variables X and Y in which the correlation is 0.42. If the level of significance is 5%, we: A) cannot test the significance of the correlation with this information. B) conclude that there is statistically significant correlation between X and Y. C) conclude that there is no significant correlation between X and Y. Correct answer is B) The calculated t is t = (0.42 × √58) / √0.8236 = 3.5246 and the critical t is approximately 2.000. Therefore, we reject the null hypothesis of no correlation. Q5. Consider a sample of 32 observations on variables X and Y in which the correlation is 0.30. If the level of significance is 5%, we: A) conclude that there is significant correlation between X and Y. B) conclude that there is no significant correlation between X and Y. C) cannot test the significance of the correlation with this information. Correct answer is B) The calculated t = (0.30 × √30) / √(1 − 0.09) = 1.72251 and the critical t values are ± 2.042. Therefore, we fail to reject the null hypothesis of no correlation. | 
发表于 2009-1-5 09:48
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