Question

A sample of 16 items from population 1 has a sample variance 5.8 and a sample of 21 items from population 2 has a sample variance 2.4. Test the following hypotheses at the .05 level of significance. H0: Population 1 Variance < Population 2 Variance Ha: Population 1 Variance > Population 2 Variance a. What is the p-value

Answer 1

Reject the null hypothesis.

Explanation:

n1 = 16

n2 = 21

S.V1 = 5.8

S.V2 = 2.4

`\alpha` = 0.05

`H_(0)` = Population Variance 1 ≤ Population Variance 2

`H_(a)` = Population Variance 1 > Population Variance 2

Test statistic value = 5.8 / 2.4 = 2.417

Degrees of freedom is n - 1

15 and 20

Critical value is
`F_(0.05)` = 2.2

2.417 > 2.2

we reject the null hypothesis as the critical value is greater than the test statistic.