.. Answer and explanation needed.
Suppose that if the null that beta equals one is true a test statistic you have calculated is distributed as a t statistic with [7 degrees of freedom. What critical value cuts off 596 of the upper tail of this distribution? 1.65 b} 134 c3195 d} 2.\" Suppose that in the previous question beta is equal to LZ. Then the critical value Front the previous question will cut off of the upper tail of the distribution of your test statistic. The blank is best lled with less than 596 b) 596 c) more than 596 Suppose that if the null that alpha and beta both equal one is true a test statistic you have calculated is distributed as a chi-square statistic with 2 degrees of freedom. What critical value cuts off 596 of the upper tail of this distribution? 3.84 b) 5.02 c1199 d) 1.3!! Suppose that if the null that alpha and beta both equal one is true a test statistic you have calculated is distributed as an F statistic with 2 and 22 degrees of freedom for the numerator and denominator respectively. What critical value cuts off 5% of the upper tail of this distribution? 3.00 b) 3.44 c1430 d) 5.72 Suppose that if the null that beta equals one is true a test statistic you have calculated is distributed as a a {standard normal) statistic. What critical value cuts off 596 of the upper tail of this distribution? IJ.3I b] 0.48 c] L55 b] 2.51 Suppose that if the null that beta equals one is tme a test statistic you have calculated is distributed as a 2 {standard normal] statistic. if you choose 1.?! as your critical value. what is your (one-sided) type [error probability? 4% b) 596 c) 696 d) 1% Suppose that ifthe null that beta equals one is true a test statistic you have calculated is distributed as a a {standard normal) statistic. If you choose 1.28 as your critical value. what is your (two-sided] type lerror probability? a)!\" b) [0% c315\") d) 10% ll. It bl A type 1 error is failing to reject the null when it is false rejecting the null when it is true The probability of a type I error is determined by the researcher the sample size the degree of falsity of the null hypothesis both b] and c) above .Atypellerroris failing to reject the null when it is false rejecting the null when it Is true . The probability of a type I! most is determined by the researcher the sample size the degree of falsity of the null hypothesis bod) b] and :1 above . Hypothesis testing is based on minimizing the type I error minimizing the type 11 error minimizing the sum of type I and type II errors none of these . A power curve graphs the degree of falseness ot' the null against the type Ierror probability the type II error probability one minus the type 1 error probability one minus the type I] error probability . When the null is true the power curve measures the type i error probability the type [I error probability one minus the type 1 error probability one minus the type 11 error probability . Other things equal. when the sample size increases the power curve flattens out becomes steeper ls unaffected . Other things equal. when the type I error probability is increased the power curve shit'ts up b] shifts down c) is unaffected 17. The power of a test statistic should become larger as the a) sample size becomes larger b) type II error becomes larger c) null becomes closer to being true d) significance level becomes smaller 18. A manufacturer has had to recall several models due to problems not discovered with its random final inspection procedures. This is an example of a) a type I error b) a type II error c) both types of error d) neither type of error 19. As the sample size becomes larger, the type I error probability a) increases b) decreases c) does not change d) can't tell 20. Consider the following two statements: a) If you reject a null using a one-tailed test. then you will also reject it using a two-tailed test at the same significance level; b) For a given level of significance, the critical value of t gets closer to zero as the sample size increases. a) both statements are true b) neither statement is true c) only the first statement is true d) only the second statement is true 21. Power is the probability of making the right decision when a) the null is true b) the null is false c) the null is either true or false d) the chosen significance level is 100% 22. The p value is a) the power b) one minus the power c) the type II error d) none of the above 23. After running a regression, the Eviews software contains a) the residuals in the resid vector and the constant (the intercept) in the c vector b) the residuals in the resid vector and the parameter estimates in the c vector c) the squared residuals in the resid vector and the constant in the c vector d) the squared residuals in the resid vector and the parameter estimates in the c vector 24. In the Eviews software, in the OLS output the intercept estimate by default is a) printed last and called "I" for "intercept" b) printed first and called "I" c) printed last and called "C" (for "constant") d) printed first and called "C" 10 25. A newspaper reports a poll estimating the proportion u of the adult population in favor of a proposition as 65%, but qualifies this result by saying that "this result is accurate within plus or minus 3 percentage points, 19 times out of twenty." What does this mean? a) the probablelty is 95% that u lies between 62% and 68% b) the probability is 95% that u is equal to 65% c) 95% of estimates calculated from samples of this size will lie between 62% and 68% d) none of the above 26. In the Eviews software, when you run an OLS regression by clicking on buttons, the parameter estimates are put in a vector called a) c (for "coefficient vector") with the first element in this vector the intercept estimate b) c (for "coefficient vector") with the last element in this vector the intercept estimate c) b (for "beta vector") with the first element in this vector the intercept estimate d) b (for "beta vector") with the last element in this vector the intercept estimate 27. A newspaper reports a poll of 400 people estimating the proportion u of the adult population in favor of a proposition as 60%, but qualifies this result by saying that "this result is accurate within plus or minus x percentage points, 19 times out of twenty." The value of x in this case is about a) 2 b) 3 c) 4 d) 5 28. In the Eviews software, in the OLS output the far right column reports a) the coefficient estimate b) the standard error c) the t value d) none of these 29. A politician wants to estimate the proportion of people in favour of a proposal, a proportion he believes is about 60%. About what sample size is required to estimate the true proportion to within plus or minus 0.05 at the 95% confidence level? a) 10 b) 100 c) 200 d) 400 30. When you calculate a 95% confidence interval for an unknown parameter beta, the interpretation of this interval is that a) the probability that the true value of beta lies in this interval is 95% b) 95% of repeated calculations of estimates of beta from different samples will lie in this interval c) 95% of intervals computed in this way will cover the true value of beta d) none of the above 31. Suppose from a very large sample you have estimated a parameter beta as 2.80 with estimated variance 0.25. Your 90% confidence interval for beta is 2.80 plus or minus approximately a) 0.41 b) 0.49 c) 0. 82 d) 0.9810 25. A newspaper reports a poll estimating the proportion u of the adult population in favor of a proposition as 65%, but qualifies this result by saying that "this result is accurate within plus or minus 3 percentage points, 19 times out of twenty." What does this mean? a) the probablelty is 95% that u lies between 62% and 68% b) the probability is 95% that u is equal to 65% ) 95% of estimates calculated from samples of this size will lie between 62% and 68% d) none of the above 26. In the Eviews software, when you run an OLS regression by clicking on buttons, the parameter estimates are put in a vector called a) c (for "coefficient vector") with the first element in this vector the intercept estimate b) c (for "coefficient vector") with the last element in this vector the intercept estimate c) b (for "beta vector") with the first element in this vector the intercept estimate d) b (for "beta vector") with the last element in this vector the intercept estimate 27. A newspaper reports a poll of 400 people estimating the proportion u of the adult population in favor of a proposition as 60%, but qualifies this result by saying that "this result is accurate within plus or minus x percentage points, 19 times out of twenty." The value of x in this case is about a) 2 b) 3 c) 4 d) 5 28. In the Eviews software, in the OLS output the far right column reports a) the coefficient estimate b) the standard error c) the t value d) none of these 29. A politician wants to estimate the proportion of people in favour of a proposal, a proportion he believes is about 60%. About what sample size is required to estimate the true proportion to within plus or minus 0.05 at the 95% confidence level? a) 10 b) 100 c) 200 d) 400 30. When you calculate a 95% confidence interval for an unknown parameter beta, the interpretation of this interval is that a) the probability that the true value of beta lies in this interval is 95% b) 95% of repeated calculations of estimates of beta from different samples will lie in this interval c) 95% of intervals computed in this way will cover the true value of beta I) none of the above 31. Suppose from a very large sample you have estimated a parameter beta as 2.80 with estimated variance 0.25. Your 90% confidence interval for beta is 2.80 plus or minus approximately a) 0.41 b) 0.49 c) 0. 82 d) 0.98 11 The next 8 questions refer to the following information. You have an estimate 1.75 of a slope coefficient which you know is distributed normally with unknown mean beta and known variance 0.25. You wish to test the null that beta = 1 against the alternative that beta > 1 at the 10% significance level. 32. The critical value to use here is a) 1.28 b) 1.65 c) 1.96 d) none of these 33. You should the null. If you had used a 5% significance level you would the null. The blanks are best filled with a) accept; accept b) accept; reject c) reject; accept d) reject; reject 34. The p value (one-sided) for your test is approximately a) 5% b) 7% c) 10% d) 23% 35. If the true value of beta is 1.01, the power of your test is approximately a) 1% b) 5% c) 10% d) nowhere near these values 36. If the true value of beta is 10.01, the power of your test is approximately a) 1% b) 5% c) 10% d) nowhere near these values 37. If the true value of beta is 1.75, the power of your test is approximately a) 10% b) 40% c) 60% d) 90% 38. If the true value of beta is 1.65, the power of your test is approximately a) 10% b) 50% c) 70% d) 90% 39. If the true value of beta is 1.25, the power of your test is approximately a) 22% b) 40% c) 60% d) 78%
