6.4 One and Two-Sample Inference for Variances

Example - Problem 26 – Page 435

D. Kim did some crude tensile strength testing on pieces of some nominally 0.012 in. diameter wire of various lengths.

Perform a hypothesis test to determine if there is a significant difference between the mean tensile strengths between 25 cm and 30 cm lengths of nominal 0.012 in. diameter wire using a significance level of 0.05.

To determine if the equal variance approach can be applied, the following hypothesis test should be performed.

Test for Equal Variances

Hypotheses

22

21

22

210

:

:

aH

H

Minitab Output

Test for Equal Variances F-Test (normal distribution) Test Statistic: 0.487 P-Value : 0.364

Levene's Test (any continuous distribution) Test Statistic: 2.710 P-Value : 0.122

0.80.70.60.50.40.30.20.1

95% Confidence Intervals for Sigmas

25cm

30cm

4.74.64.54.44.34.24.14.03.93.8

Boxplots of Raw Data

P-Value : 0.122

Test Statistic: 2.710

Levene's Test

P-Value : 0.364

Test Statistic: 0.487

F-Test

Factor Levels

30cm

25cm

Test for Equal Variances

Additional Output

Descriptive Statistics: Strength by Length Variable Length N Mean StDev Strength 25 cm 8 4.4313 0.2314 30 cm 8 4.288 0.331

Two-Sample T-Test and CI: 25cm, 30cmTwo-sample T for 25cm vs 30cm N Mean StDev SE Mean25cm 8 4.431 0.231 0.08230cm 8 4.288 0.331 0.12

Difference = mu 25cm - mu 30cm

T-Test of difference = 0 (vs not =): T-Value = 1.01 P-Value = 0.334 DF = 12

Two-Sample T-Test and CI: 25cm, 30cmTwo-sample T for 25cm vs 30cm N Mean StDev SE Mean25cm 8 4.431 0.231 0.08230cm 8 4.288 0.331 0.12

Difference = mu 25cm - mu 30cm

T-Test of difference = 0 (vs not =): T-Value = 1.01 P-Value = 0.331 DF = 14Both use Pooled StDev = 0.286