请问为什么不是跟1.996比较

问题如下：

Anna Gabor Case Scenario

Anna Gabor is an analyst with an investment management firm. She is investigating the impact of leverage on annual ROE in the firm's Eurozone equities fund ("the fund").

She collects data on the 72 stocks in the fund, including company size as an independent variable.

Exhibit 1 shows the results from estimating the model R_i = b₀ + b₁(Size_i) + b₂(D/E_i) + ε_i

Where:

• R_i is the annual ROE for company i in the last calendar year in numbers (0.05 is 5%);
• Size_i is the natural log of the market capitalization of company i (millions of Euro) on 31 December;
• D/E_i is the debt/equity ratio of company i on 31 December;
• b_o is the intercept of the equation;
• b₁, b₂ are the slope coefficients for the independent variables Size_i and D/E_i respectively;
• ε_i is the error term.

Exhibit 2 shows selected values of Student's t distribution for 69 degrees of freedom.

Gabor expects to find that both the debt/equity ratio and size are negatively related to ROE. She considers a relationship meaningful when it is statistically significant at the 0.05 level. As part of her analysis Gabor compares the predictions of her model with the actual ROE for two stocks in the portfolio which have the same debt ratio: A and B, which have market capitalizations EUR 100 million and EUR 200 million respectively.

Gabor shares her results with a colleague, Eva Szabo, who warns that the variance of the error terms might not be constant, but positively correlated with D/E and Size. Szabo states that such a flaw would lead to the F- and t-statistics being biased and failing to reject the null hypothesis when it is false.

As an additional goal Gabor investigates the impact of qualitative governance factors. She is considering adding two dummy variables, to the model: D₁ and D₂. D₁ is 1 for firms with two or more female board members, and otherwise 0. The value of D₂ is 1 if the audit committee of the board includes only independent directors, and otherwise 0. Gabor's hypothesis is that gender diversity is positively related to ROE and that an independent audit committee slows the rate at which increasing leverage affects ROE.

Finally, Gabor wishes to test the hypothesis that whether or not a stock in the fund is listed on a US (as well as European) exchange is determined by the same independent variables as above (including the governance factors). She employs a logistic regression with the dependent variable of A, which takes on a value of 1 for a company listed on a US exchange and otherwise 0. For Tekdat, a company in the fund which does not have gender diversity on its board, the probability, based on the model, of being listed on a US exchange is 0.65. The regression coefficient of D₁ in the logistic model is 0.80 and is statistically significant.

Based on Exhibits 1, 2 and Gabor's expectations, which is the best null hypothesis and conclusion regarding D/E:

Based on Exhibits 1, 2 and Gabor's expectations, which is the best null hypothesis and conclusion regarding D/E:

选项：

A.A.b₂ ≥ 0; reject the null hypothesis.

B.B.b₂ = 0; cannot reject the null hypothesis.

C.C.b₂ ≥ 0; cannot reject the null hypothesis.

解释：

• A is Correct because the null hypothesis is correctly formulated and we can reject it. Gabor expects to find that D/E is negatively related to the firm's ROE. If she is right, the regression coefficient for D/E, b₂, will be less than zero and statistically significant.

  The null hypothesis supposes that the “suspected” condition is not true, so the null hypothesis should state the variable is greater than or equal to zero. This is explained on p. 72 of the reading. Therefore we should be conducting a one-tailed test.

  The t-Statistic for b₂ is given by: -0.0172/0.0098 = -1.7551

  From Exhibit 2 we see that the critical value for a one-tailed test with 69 degrees of freedom at the 0.05 significance level is 1.667.

  So we should reject the null hypothesis if the t-statistic is less than -1.667

  Since -1.7551 < -1.667 we should indeed reject the null hypothesis.

• B is Incorrect because the null hypothesis is incorrectly formulated.

  Gabor expects to find a negative relationship between D/E and ROE that is also statistically significant. This suggests an expectation that b₂ is less than zero, leading to a null hypothesis that b₂ is greater than or equal to zero. Hence we need to conduct a one-tailed test.

  Instead, the candidate has specified a null hypothesis for a two-tailed test. This would be correct if Gabor's expectation was just that there was a statistically significant relationship between D/E and ROE, remaining neutral as to whether the relationship was positive or negative.

  With this null hypothesis, the critical value for a t-test would be 1.995, as per Exhibit 2.

  The t-Statistic for b₂ is given by: -0.0172/0.0098 = -1.7551

  Since the absolute value of this t-statistic is less than the critical value we would not be able to reject the null hypothesis. This conclusion would be correct for a two-tailed test.

  So by incorrectly specifying the null hypothesis, the candidate has also arrived at the wrong conclusion.

• C is Incorrect because, though the null hypothesis is correctly formulated, the conclusion is incorrect.

  The t-Statistic for b₂ is given by: -0.0172/0.0098 = -1.7551

  From Exhibit 2 we see that the critical value for a one-tailed test with 69 degrees of freedom at the 0.05 significance level is 1.667.

  Since -1.7551 < -1.667 we can reject the null hypothesis. Hence the conclusion is incorrect.

  A candidate who used the critical value for a one-tailed test in error would compare the t-statistic of -1.7551 with -1.995 and would have concluded that the null hypothesis cannot be rejected.