Question

17. Use the table ("Table G.2") on the last page of this examination booklet for this exercise. You want to carry out the following hypothesis test: Hot 25 H 2 5 where is the population of a normally distributed random variable (with unknown population varianceo'). The race level for this test is 0.01, your sample size is 27 and you have computed a statistic of (a) You have to compare the value-1.43 to the critical value of 2.771 (6) You have to compare the value - 143 143 to the critical of 2.479 (C) You have to compare the value - 143-143 to the critical value of 2.770 18. By definition, the causal effect of a random wariables a random variable with (a) change in variable if variable y is changed (1) change in variable y if variable is changed but all other relevant factors are held.com (c) change in variable y if all relevant factors are changing simultaneously 19. When conducting a hypothesis test, we take this hypothesis a true and require the data to provide substantial evidence against it. This hypothesis is o(a) called the alternative hypothesis. (b) called the null hypothesis. (c) the hypothesis that is commonly denoted by H - 20. You want to study the effect of the hours that a student spends sleeping every week (sleep) on his/her grade-point average (GPA). You assume a simple linear regression model for the population of the form: GPA B + sleep +. Now assume there is another variable that has an impact on GPA study, it measures the number of study hours per week. You have reason to believe that the expected value of study given 49 hours of sleep every week, differs from the expected value of study given 56 hours of sleep every week. (a) You cannot discover a causal effect of sleep on GPA by estimating your simple linear regression, because the conditional mean independence assumption is violated (b) The ordinary least squares (OLS) estimator for B is unbiased. (C) You can discover a causal effect of sleep on GPA by estimating your simple linear regression; the relation between study and sleep does not matter. 21. In hypothesis testing, the number against which a test statistic is compared to determine whether or not the null hypothesis is rejected is called (a) the ceteris paribus effect. (b) the significance level. (c) the critical value.

Answer 1

(Q 17) Ans: (c)

Since this is a two-tailed test, the critical value should be referred corresponding to 1% level of significance (alpha = 0.01) with n-1 = 27-1=26 degree of freedom. Hence, the critical value is 2.779. Therefore, correct option is (c)

(Q 18) Ans (b)

The coefficients of regression equation shows the marginal effect of change in independent variable (x) on the dependent variable (y), keeping all other factors constant, i.e., partial derivative of y with respect to x.

(Q 19) Ans (b)

While conducting hypothesis testing, we start with null hypothesis as true against an alternative hypothesis. The calculated test statistics is then compared with the critical value from appropriate table to evaluate if we can reject the null hypothesis or not. Hence, the answer is (b)

(Q 20) Ans (a)

Since study hours and sleep hours are related to each other, it violates the conditional mean independence assumptions, i.e., E(U_i|sleep) is not equal to zero. On the other hand, when this assumption is violated, OLS estimates are likely to be biased. Also, the coefficients of both the coefficients (i.e., coefficient on sleep hours and coefficient on study hours) cannot be estimated together. Hence (a) is the correct answer.

(Q 21) Ans (c)

The test statistic is compared with the critical value corresponding to a certain level of significance and appropriate degree of freedom.