Question

Assume that both samples are independent simple random samples from populations having normal distributions.

4) A researcher obtained independent random samples of men from two different towns. She recorded the weights
of the men. The results are summarized below:
Town A Town B
n1= 41 n 2 = 21
x1 = 165.1 lb x2 = 159.5 lb
s1 = 34.4 lb s2 = 28.6 lb
Use a 0.05 significance level to test the claim that there is more variance in weights of men from town A than in
weights of men from town B. Use the p-value method of testing hypotheses.

(a) Set up the null hypothesis and alternative hypothesis and indicate the claim.

(b) Calculate the test statistic. Be sure to set up the equation. Round to three decimal places.

(c) Find the p-value. Round to four decimal places.

(d) Make a decision about the null hypothesis. Be sure to explain how you make the decision.

(e) Wrrite a complete a conclusion about the original claim.

Answer 1

Sample 1:

s₁ = 34.4, n₁ = 41

Sample 2:

s₂ = 28.6, n₂ = 21

α = 0.05

a) Null and alternative hypothesis:

Hₒ : σ₁² = σ₂²

H₁ : σ₁² > σ₂²

b)

Test statistic:

F = s₁² / s₂² = 34.4² / 28.6² = 1.447

c) Degree of freedom:

df₁ = n₁-1 = 40

df₂ = n₂-1 = 20

P-value = F.DIST.RT(1.447, 40, 20) = 0.1892

d) Decision:

As p-value > α, we fail to reject the null hypothesis.

e) Conclusion:

There is not enough evidence to conclude that there is more variance in weights of men from town A than in weights of men from town B.