A company (GOGO) bench marking with the best in the industry (BANFO) has the fol

Question

A company (GOGO) bench marking with the best in the industry (BANFO) has the following defect results in batches.

Batch BANFO GOGO

1984     8.54        12.81

1985      8.31        12.47

1986       8.24        12.36

1987       7.43         11.15

1988         6.70        10.05

1989         6.53        9.80

1990         6.87       10.31

(a) Find the mean defects for each company. Which batch has the defect closest to the mean in BANFO and GOGO?

(b) Find the standard deviation for the data for both the BANFO and GOGO.

(c) In your bench marking what is your conclusion-Are the two companies having the same defect rate? (Please include the hypothesis test).

Explanation / Answer

a and b)

Variable Mean StDev Variance
GOGO 11.279 1.264 1.597
BANFO 7.517 0.843 0.711

outcome from minitab software

c) we need to test that two groups has same mean or not. So we are going to test two sample t-test

define, mu1,s1,n1 is mean , sd and sample size of gogo,

mu2 s2 n2 mean  is mean , sd and sample size of banfo

assuming the variation in two sample is same

the testing problem is to test

H0: mu1=mu2 vs H1: mu1 not equal to mu2

in minitab we have the two sample t-test is

Difference = mu (GOGO) - mu (BANFO)
Estimate for difference: 3.761
95% CI for difference: (2.510, 5.013)
T-Test of difference = 0 (vs not =): T-Value = 6.55 P-Value = 0.000 DF = 12
Both use Pooled StDev = 1.0743

here in this testing problem is p-value = 0.000 <0.05

so we reject H0 at 5% level of significance is and can claim that two sample are not same

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