Question

Consider the hypothesis test H0: = against H0: > . Suppose that the sample sizes are n1 = 20 and n2 = 8, and that = 4.5 and = 2.3. Use α = 0.01. Test the hypothesis and explain how the test could be conducted with a confidence interval on σ1/σ2.

Refer the question above test the hypothesis and provide your conclusion.

		At the alpha = 0.01, we fail to reject and conclude that the variances are the same
		At the alpha = 0.01, we reject the null and conclude that the variances are the same
		At the alpha = 0.01, we reject the null and conclude that variance 1 is larger than variance 2
		At the alpha = 0.01, we fail to reject and conclude that variance 1 is larger than variance 2

Also refer to the question above, if variance 1 is the same as variance 2, then the confidence interval on the ratio of the variances will do what?

		This is not relevant
		Both limits will be above 1
		Not include 1
		Include 1

Answer 1

using minitab>stat>two variances

we have

Test and CI for Two Variances

Method

Null hypothesis σ(First) / σ(Second) = 1
Alternative hypothesis σ(First) / σ(Second) > 1
Significance level α = 0.01

F method was used. This method is accurate for normal data only.

Statistics

99% Lower
Bound for
Sample N StDev Variance StDevs
First 20 4.500 20.250 3.261
Second 8 2.300 5.290 1.416

Ratio of standard deviations = 1.957
Ratio of variances = 3.828

99% One-Sided Confidence Intervals

Lower Bound Lower Bound
for StDev for Variance
Method Ratio Ratio
F 0.787 0.619

Tests

Test
Method DF1 DF2 Statistic P-Value
F 19 7 3.83 0.038

since p value is greater than 0.01 ,  we fail to reject and conclude that the variances are the same

if variance 1 is the same as variance 2, then the confidence interval on the ratio of the variances will include 1