Question

CHEGG Find the F-test statistic to test the claim that the variances of the two populations are equal. Both distributions are normal. The populations are independent. The standard deviation of the first sample is 6.9533 6.2248 is the standard deviation of the second sample.

Answer 1

Answer:

The F-test statistic to test the claim that the variances of the two populations are equal is 1.25.

Step-by-step explanation:

For checking the equivalence of 2 population variances of independent samples, we use the F-test.

The hypothesis is,

H₀: $\sigma_{1}^{2}=\sigma_{2}^{2}$ vs. Hₐ: $\sigma_{1}^{2}\neq \sigma_{2}^{2}$

The test statistic is given as follows:

$F=\frac{S_{1}^{2}}{S_{2}^{2}}$

It is provided that:

S₁ = 6.9533

S₂ = 6.2248

Compute the test statistic as follows:

$F=\frac{S_{1}^{2}}{S_{2}^{2}}$

   $=\frac{(6.9533)^{2}}{(6.2248)^{2}}\\\\=1.24776\\\\\approx 1.25$

Thus, the F-test statistic to test the claim that the variances of the two populations are equal is 1.25.