An investor is trying to decide whether to invest in a given

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 51 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%, what is the test statistic? (be careful on this) (please round your answer to 2 decimal places)

Solution

An investor is trying to decide whether to invest in a given stock, but is worried about the volatility of the investment.

Here we have to test the hypothesis that,

H0 : = 15% = 0.15 Vs H1 : > 0.15

Assume alpha = level of significance = 1% = 0.01

sample size (n) = 61

sample standard deviation (s) = 20% = 0.2

The Chi-square test statistic is,

X² = ((n-1)*s² ) / ²

= (61-1)*0.2² / 0.15²

X² = 106.6667

Here we have to find P-value for taking decision.

P-value we can find by using EXCEL.

syntax :

=CHIDIST(x, deg_freedom)

x is test statistic value.

deg_freedom = n-1 = 61-1 = 60

P-value = 0.000

P-value < alpha

Reject H0 at 1% level of significance.

Conclusion : Population standard deviation is higher than 15%.