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!

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following