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

mayanfang1

Q1. 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)   Chi-square test.

B)   F test.

C)   t test.

Q2. 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% 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 0.849.

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

Q3. The use of the F-distributed test statistic, F = s₁² / s₂², to compare the variances of two populations does NOT require which of the following?

A)   populations are normally distributed.

B)   two samples are of the same size.

C)   samples are independent of one another.

Q4. 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)     z-distributed.

C)     Chi-squared distributed.

[此贴子已经被作者于2009-1-13 16:17:06编辑过]

mayanfang1

答案和详解如下：

Q1. 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)   Chi-square test.

B)   F test.

C)   t test.

Correct answer is B)

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

Q2. 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% 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 0.849.

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

Correct answer is 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.

Q3. The use of the F-distributed test statistic, F = s₁² / s₂², to compare the variances of two populations does NOT require which of the following?

A)   populations are normally distributed.

B)   two samples are of the same size.

C)   samples are independent of one another.

Correct answer is B)

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

Q4. 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)     z-distributed.

C)     Chi-squared distributed.

Correct answer is A)

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

zeraeh

看答案，谢谢LZ

jacky_z

Thanks

 

One comment on Q2, if the hypothesis is σ₁² = σ₂²  which implies a two-sided test, shall we find the rejection point in F-tables at the @/2=(1-95%)/2=0.025 significance level?

[此贴子已经被作者于2009-2-25 21:07:15编辑过]

风烈

谢谢楼主～

baodexi

thx

hhzeng

kkk

hjl2000

d

connie198226

ss

kgbvvsscia

谢谢了额哈哈