Question

A study was performed to determine whether men and women differ in their repeatability in assembling components on printed circuit boards. Two samples of 25 men and 21 women were selected, and each subject assembled the units. The two sample standard deviations of assembly time were smen = 0.914 min and Swomen=1.093 min. Is there evidence to support the claim that men have less repeatability than women for this assembly task? Use alpha = 0.01 and state any necessary assumptions about the underlying distribution of the data Find a 99% lower bound on the ratio of the two variances Use at least 2 decimal digits

Answer 1

using minitab>stat>basic stat>2 variance

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 21 1.093 1.195 0.798
Second 25 1.093 1.195 0.817

Ratio of standard deviations = 1.000
Ratio of variances = 1.000

99% One-Sided Confidence Intervals

Lower Bound Lower Bound
for StDev for Variance
Method Ratio Ratio
F 0.604 0.365

Tests

Test
Method DF1 DF2 Statistic P-Value
F 20 24 1.00 0.495

99% lower bound on the ratio of two variance is 0.365