Question

An investor is trying to decide whether to invest in a given stock, but is worried about the volatility of the investment. If the investor is very certain that the volatility (as measured by the standard deviation) is greater than 15% then the investor will choose a different investment option. In a sample of the previous 101 days reveals that the standard deviation of the investment is 20%. When testing the hypothesis (at the 1% level of significance) that the standard deviation is higher than 15% (or variance is greater than 225), what is the null and alternative hypotheses? (please write out the null and alternative hypotheses below AND on your scratch work...failure to do BOTH will result in 0 points)

Also test statisic of this problem?

Answer 1

Solution:

Given

n= 101 sample size

population standard deviations

s = 20% sample standard deviations

level of significance.

To test the hypothesis

. Vs.   

Test statistic

Test statistic

P Value =0.00001 from online P value calculator

Decision: P value <

0.00001< 0.01

Reject Ho

Conclusion : Reject Ho, there is sufficient evidence to conclude that Standard deviations higher than 15% or variance greater than 225.