Question

In order to test the equality of variances in the yield per plant of two varieties, two independent random samples, one for each variety of plants were selected leading to the following summary results: Variaty Number of Plants Total Yield Sum of Squares of Yield 1 10 240 5823 2 12 276 6403 Is the claim of equality of variances supported by the data? Use α = 0.05. Assume the two populations to be normally distributed. [5 Marks

Answer 1

Solution:

Here, we have to use F test for equality of two population variances. The null and alternative hypotheses for this test are given as below:

Null hypothesis: H₀: Two population variances are same.

Alternative hypothesis: H_a: Two population variances are not same.

H₀: σ1^2 = σ2^2 versus H_a: σ1^2 ≠ σ2^2

This is two tailed test.

We are given

Level of significance = α = 0.05

We have

S^2 = SS/(n – 1)

We are given

SS for yield 1 = 5823

n1 = 10

S1^2 = 5823/(10 – 1) = 5823/9 = 647

SS for yield 2 = 6403

n2 = 12

S2^2 = 6403/(10 – 1) = 6403/9 = 711.4444

Test statistic is given as below:

F = S2^2/S1^2 = 711.4444/647 = 1.09960495

Test statistic = F = 1.0996

df1 = n1 – 1 = 12 – 1 = 11

df2 = n2 – 1 = 10 – 1 = 9

Critical value = 3.9121

(by using F-table)

P-value = 0.9014

(by using F-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

There is sufficient evidence to conclude that two population variances are same.