F test for variance ($H_0 : σ_1^2 ≤ σ_2^2$)
$begingroup$
Consider two different normal distributions for which both the means $µ_1$
and $µ_2$ and the variances $σ_1^2$ and $σ_2^2$ are unknown, and suppose that it is
desired to test the following hypotheses:
$H_0 : σ_1^2 ≤ σ_2^2$
$H_1 : σ_1^2 ≥ σ_2^2$
Where $S_1^2=8.13$ and $S_2^2=4.4$
Sample size $n_1=16$ and $n_2=10$
(a) Test the hypotheses at the level of significance 0.05.
(b) Find the power function of the test when $σ_1^2=2σ_2^2$
I know how I can solve these kind of problem when $H_0$ is simple.
However, under $H_0 : σ_1^2 ≤ σ_2^2$, with inequality, I don't know what should be done here.
hypothesis-testing
asked Dec 4 '18 at 17:04
NewtNewt
207
$endgroup$
add a comment |
$begingroup$
Consider two different normal distributions for which both the means $µ_1$
and $µ_2$ and the variances $σ_1^2$ and $σ_2^2$ are unknown, and suppose that it is
desired to test the following hypotheses:
$H_0 : σ_1^2 ≤ σ_2^2$
$H_1 : σ_1^2 ≥ σ_2^2$
Where $S_1^2=8.13$ and $S_2^2=4.4$
Sample size $n_1=16$ and $n_2=10$
(a) Test the hypotheses at the level of significance 0.05.
(b) Find the power function of the test when $σ_1^2=2σ_2^2$
I know how I can solve these kind of problem when $H_0$ is simple.
However, under $H_0 : σ_1^2 ≤ σ_2^2$, with inequality, I don't know what should be done here.
hypothesis-testing
asked Dec 4 '18 at 17:04
NewtNewt
207
$endgroup$
add a comment |
$begingroup$
Consider two different normal distributions for which both the means $µ_1$
and $µ_2$ and the variances $σ_1^2$ and $σ_2^2$ are unknown, and suppose that it is
desired to test the following hypotheses:
$H_0 : σ_1^2 ≤ σ_2^2$
$H_1 : σ_1^2 ≥ σ_2^2$
Where $S_1^2=8.13$ and $S_2^2=4.4$
Sample size $n_1=16$ and $n_2=10$
(a) Test the hypotheses at the level of significance 0.05.
(b) Find the power function of the test when $σ_1^2=2σ_2^2$
I know how I can solve these kind of problem when $H_0$ is simple.
However, under $H_0 : σ_1^2 ≤ σ_2^2$, with inequality, I don't know what should be done here.
hypothesis-testing
asked Dec 4 '18 at 17:04
NewtNewt
207
$endgroup$
Consider two different normal distributions for which both the means $µ_1$
and $µ_2$ and the variances $σ_1^2$ and $σ_2^2$ are unknown, and suppose that it is
desired to test the following hypotheses:
$H_0 : σ_1^2 ≤ σ_2^2$
$H_1 : σ_1^2 ≥ σ_2^2$
Where $S_1^2=8.13$ and $S_2^2=4.4$
Sample size $n_1=16$ and $n_2=10$
(a) Test the hypotheses at the level of significance 0.05.
(b) Find the power function of the test when $σ_1^2=2σ_2^2$
I know how I can solve these kind of problem when $H_0$ is simple.
However, under $H_0 : σ_1^2 ≤ σ_2^2$, with inequality, I don't know what should be done here.
hypothesis-testing
hypothesis-testing
asked Dec 4 '18 at 17:04
NewtNewt
207
asked Dec 4 '18 at 17:04
NewtNewt
207
asked Dec 4 '18 at 17:04
NewtNewt
207
asked Dec 4 '18 at 17:04
NewtNewt
207
asked Dec 4 '18 at 17:04
NewtNewt
207
207
add a comment |
add a comment |
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