Question

Identify the critical value F₀ to test the claim that   σ_{1^{2 ≤}} σ_2² . Random samples of size n₁ = 16 and n₂ = 15 are chosen. Use α = .05. ^_.  

		2.46
		3.66
		2.95
		2.40

Identify the critical value F₀ to test the claim that   σ_{1^{2 ≠}} σ_2² . Random samples of size n₁ = 11 and n₂ = 18 are chosen. Use α = .02.

		3.59
		2.45
		2.92
		4.56

Non-parametric tests, unlike parametric ones, do not make assumptions about

		the underlying distribution shape
		the sample size
		the sample statistics
		the population size

Answer 1

1)

Answer: 2.46

Explanation: The critical value for the F-statistic is obtained from F-distribution table for significance level = 0.05 and numerator degree of freedom = n₁-1= 16-1=15 and denominator degree of freedom = n₂-1= 16-1=15 for one tailed alternative hypothesis

2)

Answer: 3.59

Explanation: The critical value for the F-statistic is obtained from F-distribution table for significance level = 0.02 and numerator degree of freedom = n₁-1= 11-1=10 and denominator degree of freedom = n₂-1= 18-1=17 for two tailed alternative hypothesis.

3)

Answer: the underlying distribution shape

Explanation: The non-parametric test is used when we do not know the distribution of the data.