Question

Soru 1. One risky and one prudent, two investment startegies are compared. 7 of the funds following the first strategy have average return of 15% with standard deviation of 12%. 15 of the funds that follow the second strategy have an average return of 12% with standard deviation of 9%. What are the calculated and critical test statistics and the test result? (alpha=5%, consider one sided test that one of the varances is higher) A 1.58, 285, do not reject Ho B 1.58, 2.71, do not reject Ho C 2.58, 2.71, reject Ho D 2.58, 2.85, reject Ho

Answer 1

Correct option:

A.   1.78, 2.85, do not reject H0.

H0: Null Hypothesis: $\sigma 1^{2}\leq \sigma 2^{2}$

HA: Alternative Hypothesis: $\sigma 1^{2}>\sigma 2^{2}$

s1 = 12

s2 = 9

n1 = 7

n2 = 15

$\alpha$ =0.05

df1 = n1- 1 = 7- 1 = 6

df2 = n2 - 1 = 15 - 1 = 14

One Tail - Right Side Test

From Table, critical value of FU = 2.85

Test Statistic is gven by:

$F=\frac{s1^{2}}{s2^{2}}=\frac{12^{2}}{9^{2}}=1.78$

Since calculated value of F = 1.78 isless than critical value of F = 2.85, the difference is not significant. Fail to reject null hypothesis.