The following hypotheses are given. h0 : σ1² ≤ σ2² h1 : σ1² > σ2² a random sample of five observations from the first population resulted in a standard deviation of 12. a random sample of seven observations from the second population showed a standard deviation of 7. at the 0.01 significance level, is there more variation in the first population?

Desision is to not reject the null hypothesis, this means that the variance of the second population is equal or greater than the variance of the first population.

Step-by-step explanation:

Hello!

You have the hypothesis set:

H₀: δ₁² ≤ δ₂²

H₁:  δ₁² > δ₂²

α: 0.01

To study the population variance of two populations you have to work with the F-distribution. The statistic is:

F= (S₁²/S₂²)*(σ₁²/σ₂²) ~ F

This is a one tailed test, the critical value is

If the statistic value F ≥ 9.15, the decision is to reject the null hypothesis.

If the value F < 9.15, the decision is to not reject the null hypothesis.

F=  (S₁²/S₂²)*(σ₁²/σ₂²) = (12/7) * 1

F= 1.714

Desision is to not reject the null hypothesis, this means that the variance of the second population is equal or greater than the variance of the first population.

I hope you have a SUPER day!

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get