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Microsoft Word - Ecom2000_Q1_Practice_2017_v2.docx 1 ECOM2000 – PRACTICE QUIZ 1 Some notes: Actual Quiz will be given online. It will be in a similar format with this practice quiz (10 questions, all in multiple choice format). You are allowed to use calculators. 1. If X N(2, 4), then a. X is normally distributed with mean 2 and variance 4. b. X is normally distributed with mean 2 and variance 2. c. X is normally distributed with mean 4 and variance 2. d. X is normally distributed with mean 2 and variance 16. 2. Suppose that you want to test H0: = 0 against HA: > 0. Which of the following is the rejection rule for this one‐sided hypothesis test? a. ttest < tcritical b. ="" ttest =""> tcritical c. |ttest| < tcritical d. ="" |ttest| =""> tcritical 3. Let X be a random variable representing hourly wage that university students receive for their part‐time work. Suppose that the population mean of X is $18 and the standard deviation is 6. If the sample mean is calculated for randomly sampled 100 students, what will be the variance of the sample mean? a. 0.060 b. 0.360 c. 0.364 d. 0.600 4. Suppose that 76% of college students in Australia use more than 1.65 gigabytes of data on their mobile phone per month. If the monthly mobile data usage by college students is normally distributed with variance of 2.25, what will be the average mobile data usage? a. 0.061 b. 0.591 c. 2.709 d. 3.239 5. Suppose that you want to test if the population mean of a random variable X is equal to 150 (that is, H0: = 150) against two‐sided alternative of ≠ 150. Suppose further that for a sample of 50 observations, you calculated the t‐test statics of 2.325. Given that the two relevant critical values are: T.INV.2T(0.05, 49) = 2.010 and T.INV.2T(0.01, 49) = 2.680, which of the following conclusions is correct? a. Reject H0 at the 5% size, but not at the 1% size. b. Reject H0 at the 1% size, but not at the 5% size. c. Reject H0 both at the 5% size and at the 1% size. d. Reject H0 neither at the 5% size nor at the 1% size. 2 6. Which of the following provides a correct interpretation of the parameter in a linear regression model, Yi = 0 + 1Xi + i? a. 0 represents the marginal effect of x on y b. 1 represents the marginal effect of x on y c. 0 represents the marginal effect of y on x d. 1 represents the marginal effect of y on x 7. Suppose that a linear regression equation is estimated as Yi = 15000 − 750 Xi + ei. What is the predicted value of the Y when the explanatory variable is X = 12? a. 6,000 b. 14,238 c. 14,262 d. 171,000 8. Which of the following best describes the explained sum of squares (SSE) for a simple linear regression model, Yi = b0 + b1X + ei? a. It represents the total variation of the dependent variable Y. b. It represents the total variation of the explanatory variable X. c. It represents the part of the variation in the dependent variable Y that is explained by the estimated regression function. d. It represents the part of the variation in the dependent variable Y that is not explained by the estimated regression function. 9. Which of the following is part of the six assumptions of the Linear Regression Model? a. The error term i has an expected value of 1 for all individuals i = 1, …, n. b. The error term i has an expected value of 0 for all individuals i = 1, …, n. c. The variance of the error term i is 1 for all individuals i = 1, …, n. d. The explanatory variable X has the same value for all individuals in a sample. 10. Suppose that in a simple linear regression model of wage on education, Wagei = 0 + 1Edui + i, the variance of the error term is greater for individuals with more years of education. This violates which of the following assumptions of the Linear Regression Model? a. The linear model correctly specifies the true population relationship between the dependent and explanatory variable. b. The explanatory variable is not correlated with the error term. c. The error term is homoskedastic, i.e., has the constant variance for all individuals. d. The error term has an expected value of zero for all individuals. ANSWERS: 1 – a, 2 – b, 3 – b, 4 – c, 5 – a, 6 – b, 7 – a, 8 – c, 9 – b, 10 – c. 3 ADDITIONAL PRACTICE QUESTIONS 11. Suppose that you want to test H0: = 0 against HA: ≠ 0. Which of the following is the rejection rule for this hypothesis test? a. ttest < tcritical b. ="" ttest =""> tcritical c. |ttest| < tcritical d. ="" |ttest| =""> tcritical 12. How can a normally distributed random variable X N(, 2) be converted into the standard normal distribution? a. By subtracting the mean from X and multiplying by the standard deviation . b. By adding the mean to X and multiplying by the standard deviation . c. By subtracting the mean from X and dividing by the standard deviation . d. By adding the mean to X and dividing by the standard deviation . 13. Which of the following statements would you consider to be correct concerning the normal distribution? a. Bell‐shaped and symmetrical around zero. b. Has a mean of zero and a variance of one. c. Becomes more spread out as its variance increases. d. All of the above. 14. Which of the following statements is true about how the sample variance of X affects the confidence interval of the population mean? a. When the sample variance of X increases, the confidence interval of the population mean narrows down. b. When the sample variance of X increases, the confidence interval of the population mean widens. c. The sample variance of X has no effect on the confidence interval of the population mean. d. Change in the confidence interval of the population mean, when the sample variance of X increases, is indeterminant. 15. The OLS estimator of slope coefficient in the linear regression model, Y = 0 + 1X + , can be expressed as, a. Cov(X, Y) b. Cov(X,Y)/Var(X) c. Cov(X,Y)/Var(Y) d. None of the above 16. Which of the following best describes the residual sum of squares (SSR) for a simple linear regression model, Y = b0 + b1X + e? a. It represents the total variation of the dependent variable Y. b. It represents the total variation of the explanatory variable X. c. It represents the part of variation in the dependent variable Y that is explained by the estimated regression function. d. It represents the part of variation in the dependent variable Y that is not explained by the estimated regression function. 4 17. Suppose that a linear regression equation is estimated as Y = 125 + 50X + e. For an individual with X = 20 and Y = 1200, what is the values of the regression residual? a. 75 b. ‐75 c. 1125 d. 1200 18. Which of the following statements is not part of the six assumptions of the Linear Regression Model? a. The model, Y = 0 + 1X + , correctly specifies the true relationship between Y and X in population. b. The error term is not correlated between any pairs of individuals, that is, cor(i, j) = 0 for any i ≠ j. c. The error term is normally distributed. d. The error term i has an expected value of zero for all individuals i = 1, …, n. 19. When is the error term in a regression equation said to exhibit homoskedasticity? a. If its expected value is zero for all individuals in a sample. b. If it has the same variance for all individuals in a sample. c. If it has the same value for all individuals in a sample. d. If it is uncorrelated with the explanatory variable. 20. The OLS estimator of the slope coefficient in a simple linear regression model, Y = 0 + 1X + , is normally distributed if: a. the error term is normally distributed with mean 0 and variance 2 b. sample size (n) is large (greater than 30) c. both A and B d. either A or B or both ANSWERS: 11 – d, 12 – c, 13 – c, 14 – b, 15 – b, 16 –d, 17 –a, 18 – c, 19 – b, 20 – d.