Question

1. (NOTE: This exercise is an exception to the no-by-hand-work rule. Here, you must type in answers to all parts of the exercise.) We wish to compare the variances of two populations. We take random samples from each with the following results:

Sample 1: n = 18, sample standard deviation = 18.9

Sample 2: n = 29, sample standard deviation = 12.6

We wish to use the F test to test whether the population standard deviations are equal.

1. What are the hypotheses for a 1-sided F test?
2. What is the F statistic for this test?
3. What are the degrees of freedom (numerator and denominator) for this test?
4. The critical value for a 1-sided F test based on these samples at α = 0.05 is 2.003. Given this and assuming a valid test, do the 1-sided test by hand; that is, considering the F statistic computed in part b, state the conclusion of this test.

Now, use Minitab to conduct the test. (Use 2-Variances with Sample Standard Deviations.) Interpret the corresponding ratio confidence bound for this test. REMEMBER to copy and paste the relevant Minitab output to your paper.

Answer 1

output of the minitab

Test and CI for Two Variances

Method

Null hypothesis σ(First) / σ(Second) = 1
Alternative hypothesis σ(First) / σ(Second) > 1
Significance level α = 0.05

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

Statistics

95% Lower
Bound for
Sample N StDev Variance StDevs
First 18 18.900 357.210 14.837
Second 29 12.600 158.760 10.370

Ratio of standard deviations = 1.500
Ratio of variances = 2.250

95% One-Sided Confidence Intervals

Lower Bound Lower Bound
for StDev for Variance
Method Ratio Ratio
F 1.060 1.123

Tests

Test
Method DF1 DF2 Statistic P-Value
F 17 28 2.25 0.028

## from p value we can say that : we reject Ho if p value is less than alpha value here p value is less than alpha value
### we reject Ho ie population standard deviation is not equal .