An investor is considering two types of investment. She is quite satisfied that

Question

An investor is considering two types of investment. She is quite satisfied that the expected profit margin on Investment 1 is higher than the expected profit margin on Investment 2. However, she is quite concerned that the risk associated with Investment 1 is higher than that of Investment 2. To help make her decision, she randomly selects seven monthly profit margins on investment I and ten monthly profit margins on investment 2. She finds that the sample variances of Investments I and 2 arc 225 and 118, respectively. Can she infer at the 5% significance level that the population variance of investment 1 exceeds that of investment 2?

Explanation / Answer

We will use F-test to check the difference between variances of both investments

given,

n1=7, v1=225

n2=10, v2=118

hypothesis formation

H0: v1<=v2

Ha: v1>v2 (one-sided F-test)

F-stat= v1/v2 = 225/118= 1.9068 with 7 & 10 df for numerator and denominator

at 5% level F(7,10) critical= 3.135 {from F-table}

Since

F-stat < F_critical at 5% level, so we cant reject H0.

means there is no evidence to state that variance of investment 1 exceeds that of investment-2.

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