Question

Suppose you are an expert on the fashion industry and wish to gather information to compare the amount earned per month by models featuring Liz Claiborne attire with those of Calvin Klein. The following is the amount ($000) earned per month by a sample of 15 Claiborne models: $3.9 $4.2 $5.1 $5.9 $6.4 $6.6 $6.4 $5.5 $3.8 $4.5 4.5 6.9 3.7 5.0 6.7

The following is the amount ($000) earned by a sample of 12 Klein models. $4.6 $4.2 $5.2 $5.1 $4.8 $3.9 $4.0 $4.2 $3.6 $3.9 4.3 4.4

b. State the decision rule for 0.10 significance level: H0: μClaiborne ≤ μCalvin Klein ; H1: μ Claiborne > μ Calvin Klein. (Round your answer to 3 decimal places.)

Answer 1

the null and alternative hypothesis is

H0: μClaiborne ≤ μCalvin Klein ;

H1: μ Claiborne > μ Calvin Klein.

using minitab>stat>basic stat>two sample t

we have

Two-Sample T-Test and CI: Claiborne models, Klein models

Two-sample T for Claiborne models vs Klein models

N Mean StDev SE Mean
Claiborne models 15 5.27 1.15 0.30
Klein models 12 4.325 0.526 0.15

Difference = μ (Claiborne models) - μ (Klein models)

Estimate for difference: 0.923
95% CI for difference: (0.235, 1.611)
T-Test of difference = 0 (vs ≠): T-Value = 2.81 P-Value = 0.011 DF = 19

b ) t at 90% confidence with 19df is 1.328 So we reject Ho if t < 1.328