Question

and with minitab please.

4. Consider the hypothesis test Ho: o? =ož vs. H: 0}<03. Suppose that the sample sizes are nl = 5 and n2 = 10, and that S -23.2 and 53-28. Test this hypothesis using 5% significance.

Answer 1

Given

s₁² = 23.2, n₁ = 5, df₁ = 5-1 = 4

s₂² = 28, n₂ = 10, df₂ = 10-1 = 9

The Hypothesis:

H0: : There is no difference in variation between the prices of Fusion Hybrid and Ford Focus.

q; = q;

Ha: : The variation in the price of Fusion Hybrid is greater than that of Ford Focus.

vi < o;

The Test Statistic:

F = s₁²/s₂² = 23.2 / 28 = 0.83

The Critical Value at $\alpha$ = 0.05, df1 = 4, df2 = 9 is 0.167

The p value: The p value (left tail) = 0.4614

The Decision Rule: If Fobserved is < F critical, Then reject H0.

Also if p value is < $\alpha$ , Reject H0.

The Decision: Since Fobserved (0.83) is > Fcritical, we fail to reject H0.

Also since p value is > 0.05, we fail to reject H0.

The Conclusion: There is insufficient evidence at the 95% significance level to conclude that the variation in population 1 is lesser than that of population 2.