When the necessary conditions are met, a two-tail test is being conducted at $\alpha$ = 0.025 to test
H₀: $\sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 }$ = 1. The two sample variances are $s _ { 1 } ^ { 2 }$ = 375 and $s _ { 2 } ^ { 2 }$ = 625, and the sample sizes are
n₁ = 36 and n₂ = 36. The calculated value of the test statistic will be F = 0.60.

Question

When the necessary conditions are met, a two-tail test is being conducted at

\alpha

= 0.025 to test
H₀:

\sigma _ { 1 } ^ { 2 } / \sigma _ { 2 } ^ { 2 }

= 1. The two sample variances are

s _ { 1 } ^ { 2 }

= 375 and

s _ { 2 } ^ { 2 }

= 625, and the sample sizes are
n₁ = 36 and n₂ = 36. The calculated value of the test statistic will be F = 0.60.

Quizplus · Accepted Answer

The calculated value of the test statistic is F = 0.60, which is less than the critical value of F = 3.24 at $\alpha$ = 0.025 and degrees of freedom (35, 35). Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the variances of the two populations are different.

When the Necessary Conditions Are Met, a Two-Tail Test Is α\alphaα

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