Question

1. Single Factor Anova is used to decide whether risk level should be regarded as a source of mutual fund return variation. Three levels of risk are employed: low, medium and high. The annual % return for random samples of 10 funds at each risk level is recorded. State the hypotheses of the test using correct notation and complete sentences.

a) In a complete sentence (using the terms ‘risk level’ and ‘return’) explain the decision that would correspond to a Type 1 error in this context. (1)

b) Do the same for Type 2 error.

2. a) For the same question, in a complete sentence, explain the conclusion that is consistent with a p-value of 0.34.

b) For the same question, in a complete sentence, explain the conclusion that is consistent with a p-value of 0.004.

3. In a complete sentence, explain, with great logical clarity, the idea represented by the ANOVA partition of variation SST = SSB + SSW. Do not simply give the words that the symbols represent.

4. Suppose all the dfs are the same for these two bits of Anova output. Which test yields the smaller p-value? i) SST = 400, SSB = 300, SSW = 100 vs. ii) SST = 400, SSB = 100, SSW = 300 Your answer must explain why and be in the form of a complete sentence

5. a) Explain in a complete sentence what the coefficient of correlation measures.

b) Show your calculation of r for this data set. (4) // 1

x = 5,3,1

y= 6,12,12

Answer 1

Null hypothesis H0: . That is, mean annual % return is equal for all risk levels.

Alternative hypothesis Ha: At least one of the means is not equal with others. That is, mean annual % return is not equal for all risk levels.

a)

Type I error is to reject null hypothesis H0 but in reality, mean annual % return is equal for all risk levels.

b)

Type I| error is fail to reject null hypothesis H0 but in reality, mean annual % return is not equal for all risk levels.

2.

a)

Since, p-value is greater than 0.05 significance level, we fail to reject null hypothesis H0 and conclude that there is no strong evidence that mean annual % return is not equal for all risk levels.

b)

Since, p-value is less than 0.05 significance level, we reject null hypothesis H0 and conclude that there is a strong evidence that mean annual % return is not equal for all risk levels.