Question

H0:σ^2 (1) ≤σ^2 (2), HA:σ^2 (1)>σ^2 (2)

n(1) = 15, s^2 (1) = 1000;

n(2) = 27, s^2 (2) = 689

α=0.05

Reject or do not reject H0?

Answer 1

Solution :

The null and alternative hypotheses are as follows :

Test statistic :

To test the hypothesis the most appropriate test is F-test for testing the equality of two population variances. The test statistic is given as follows :

Where, s_{​​​​​​1}^{​​​​​2} and s_{​​​​​​2}² are sample variances.

We have, s_{​​​​​​1}^{​​​​​2} = 1000 and s_{​​​​​​2}² = 689

The value of the test statistic is 1.4514.

Degrees of freedom = (n1 - 1, n2 - 1) = (15 - 1, 27 - 1)

Degrees of freedom = (14, 26)

P-value :

Since, our test is right-tailed test, therefore we shall obtain right-tailed p-value for the test statistic. The right-tailed p-value is given as follows :

P-value = P(F > value of the test statistic)

P-value = P(F > 1.4514)

P-value = 0.1993

The p-value is 0.1993.

Conclusion :

α=0.05 and p-value = 0.1993

Since, p-value is greater than α=0.05, therefore do not reject H_{​​​​​​0}.

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