Question

Whonose Economic Forecasting, Inc. and Wazzup Econometrics have the same mean error per year in forcasting the stock market over the last ten years. However, the standard deviation for Whonose is 40 points and 30 points for Wazzup. At the 0.05 significance level can we conclude that there is a difference in the variation?

Answer 1

Null hypothesis: Ho       σ1	=	σ2
Alternate Hypothesis: Ha        σ2	≠	σ2

	n1    =	10
	n2    =	10
df of numerator v1 =n1-1=		9
df of denominator v2=n2-1 =		9

for 5 % level and given df critical values of F      =0.248 & 4.026

Decision rule:reject Ho if test statistic F in critical region:0.248 <F> 4.026

Test statistic =s12/s22 =(40/30)^2 =

1.78

since test statistic does not falls in rejection region we fail to reject null hypothesis

we do not have have sufficient evidence to conclude that  there is a difference in the variation