Question

Consider the following data from two independent samples. Assume that the populations are normally distributed.

Sample 1

Sample 2

Sample mean: 68.7

Sample mean: 75.1

s1 = 12.5

s2 = 11.8

n1=10

n2=14

Is there evidence that the population variances are different? a=0.03

1. My question is what are the hypothesis?

None of these options

2.Which of the following statements are true?

Critical values for this test are 0.2230 and 3.7884
The value of the test statistic is 1.1222
The p-value is 0.8244
Reject Ha and conclude there is sufficient evidence to conclude that population variances are different.

Answer 1

Sample 1: s₁ = 12.5, n₁ = 10

Sample 2: s₂ = 11.8, n₂ = 14

α = 0.03

Null and alternative hypothesis:

Hₒ : σ₁ = σ₂ ; H₁ : σ₁ ≠ σ₂

Test statistic:

F = s₁² / s₂² = 12.5² / 11.8² = 1.1222

Degree of freedom:

df₁ = n₁-1 = 9

df₂ = n₂-1 = 13

Critical value(s):

Lower tailed critical value, Fα/₂ = F.INV(0.03/2, 9, 13) = 0.2230

Upper tailed critical value, F₁-α/₂ = F.INV(1-0.03/2, 9, 13) = 3.7884

P-value :

P-value = 2*F.DIST.RT(1.1222, 9, 13) = 0.8244

Conclusion:

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

True statements:

• Critical values for this test are 0.2230 and 3.7884
• The value of the test statistic is 1.1222
• The p-value is 0.8244