The F-hypothesis test is defined for this question as:
"H_0: \u03c3_1^2 = \u03c3_2^2"
"H_1: \u03c3_1^2 > \u03c3_2^2"
Given that,
"n_1=9,n_2=12"
"s_1^2 = 20,s_2^2=8"
F test statistic, "=s_1^2 \/ s_2^2"
"=20\/8=2.5"
a) For "\\alpha=0.005" and degree of freedoms "(8,11)"
Critical region will be "F>F(\\alpha,n_1-1,n_2-1)"
"F(\\alpha,n_1-1,n_2-1)=F(0.005,8,11)=5.6821"
So, the critical region is "F>5.6821"
Since the test statistics does not fall in the critical region, null hypothesis cannot be rejected. So, there is not enough evidence to show that first variance is larger than the second variance.
b) For "\\alpha=0.001" and degree of freedoms "(8,11)"
Critical region is "F>8.354"
Since the test statistics does not fall in the critical region, null hypothesis cannot be rejected. So, there is not enough evidence to show that first variance is larger than the second variance.
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