#### SamuelMartin

##### New Member

Thank you very much

Question: sample question from GARP

SunStar is a mutual fund with a stated objective of controlling volatility, as measured by the standard

deviation of monthly returns. Given the information below, you are asked to test the hypothesis that the

volatility of SunStar’s returns is equal to 5%.

Mean Monthly Return 2.5%

Monthly Standard Deviation 4.9%

Number of Observations 30

What is the correct test to be used and what is the correct conclusion at the 5% level of significance?

a. Chi-Square test; reject the hypothesis that volatility is 5%.

b. Chi-Square test; do not reject the hypothesis that volatility is 5%.

c. t-test; reject the hypothesis that volatility is 5%.

d. t-test; do not reject the hypothesis that volatility is 5%.

Answer: b

Explanation: Since you are trying to test population variance, it is appropriate to use the Chi-Square test for the

equality of two variances:

Ho : σ2 = .0025

H1 : σ2 ≠ .0025

For 29 observations, Chi square values at probability of 0.975 and .025 are 16.04707 and 45.72229. We reject the

hypothesis if computed value is <16.04707 or >45.72229.

Since the computed value is 27.84 we do not reject the hypothesis that sample standard deviation is 5%

Topic: Quantitative Analysis

Subtopic: Statistical inference and hypothesis testing

AIMS: Define and interpret the null hypothesis and the alternative hypothesis. Define, calculate and interpret

chi-squared test of significance

Reference: Damodar Gujarati, Essentials of Econometrics, 3rd Edition (McGraw‐Hill, 2006), Chapter 5