Reading 11: Hypothesis Testing - LOS f, (Part 2) ～ Q1-4 black, class

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答案和详解如下：

1.The test of the equality of the variances of two normally distributed populations requires the use of a test statistic that is:

A)   F-distributed.

B)   Chi-squared distributed.

C)   t-distributed.

D)   z-distributed.

The correct answer was A)

The F-distributed test statistic, F = s₁² / s₂², is used to compare the variances of two populations.

2.The use of the F-distributed test statistic, F = s₁² / s₂², to compare the variances of two populations requires all of the following EXCEPT:

A)   two samples are of the same size.

B)   samples are independent of one another.

C)   populations are normally distributed.

D)   larger variance in the numerator in the calculation.

The correct answer was A)

The F-statistic can be computed using samples of different sizes. That is, n₁ need not be equal to n₂.

3.Abby Ness is an analyst for a firm that specializes in evaluating firms involved in mineral extraction. Ness believes that the earnings of copper extracting firms are more volatile than those of bauxite extraction firms. In order to test this, Ness examines the volatility of returns for 31 copper firms and 25 bauxite firms. The standard deviation of earnings for copper firms was $2.69, while the standard deviation of earnings for bauxite firms was $2.92. Ness’s Null Hypothesis is σ₁² = σ₂². Based on the samples, can we reject the null hypothesis at a 95 percent confidence level using an F-statistic and why? Null is:

A)   not rejected. The critical value exceeds the F-value by 0.71.

B)   rejected. The F-value exceeds the critical value by 0.71.

C)   rejected. The F-value exceeds the critical value by 0.849.

D)   not rejected. The critical value exceeds the F-value by 0.194.

The correct answer was A)    

F = s₁² / s₂² = $2.92² / $2.69² = 1.18

From an F table, the critical value with numerator df = 24 and denominator df = 30 is 1.89.

4.In order to test if Stock A is more volatile than Stock B, prices of both stocks are observed to construct the sample variance of the two stocks. The appropriate test statistics to carry out the test is the:

A)   F test.

B)   t test.

C)   Z test.

D)   Chi-square test.

The correct answer was A)    

The F test is used to test the differences of variance between two samples.

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1.The test of the equality of the variances of two normally distributed populations requires the use of a test statistic that is:

A)   F-distributed.

B)   Chi-squared distributed.

C)   t-distributed.

D)   z-distributed.

2.The use of the F-distributed test statistic, F = s₁² / s₂², to compare the variances of two populations requires all of the following EXCEPT:

A)   two samples are of the same size.

B)   samples are independent of one another.

C)   populations are normally distributed.

D)   larger variance in the numerator in the calculation.

3.Abby Ness is an analyst for a firm that specializes in evaluating firms involved in mineral extraction. Ness believes that the earnings of copper extracting firms are more volatile than those of bauxite extraction firms. In order to test this, Ness examines the volatility of returns for 31 copper firms and 25 bauxite firms. The standard deviation of earnings for copper firms was $2.69, while the standard deviation of earnings for bauxite firms was $2.92. Ness’s Null Hypothesis is σ₁² = σ₂². Based on the samples, can we reject the null hypothesis at a 95 percent confidence level using an F-statistic and why? Null is:

A)   not rejected. The critical value exceeds the F-value by 0.71.

B)   rejected. The F-value exceeds the critical value by 0.71.

C)   rejected. The F-value exceeds the critical value by 0.849.

D)   not rejected. The critical value exceeds the F-value by 0.194.

4.In order to test if Stock A is more volatile than Stock B, prices of both stocks are observed to construct the sample variance of the two stocks. The appropriate test statistics to carry out the test is the:

A)   F test.

B)   t test.

C)   Z test.

D)   Chi-square test.