Hypotheis Testing of stock return

Question

An analyst wants to test whether the standard deviation of return from pharmaceutical stocks is

lower than 0.2. For this purpose, he obtains the following data from a sample of 30

pharmaceutical stocks. Mean return from pharmaceutical stocks = 8%. Standard deviation of

return from pharmaceutical stocks = 12%. Mean return from the market = 12%. Standard

deviation of return from the market = 16%. Based on this information, we can say that at a

Answer 1

 First thing first. This question is related to hypothesis of variance .We will use chi square test to verify this claim

H_a: V_o < (0.2)² 

H₀: V₀>= (0.2)² 

. Its a left side test .at 0.005(.5%) significance level with 29 Degree of Freedom(we will look for value corresponding to 99.5% against 29 ,   the critical value is  around 15

our test Stats is = (n-1) x S² / V₀² = 29 x .12x.12/(0.2 x0.2)=  10.44. our test stats is  below critical level .so we will reject the null and accept that  SD is less than 0.2