Question

Two suppliers manufacture a plastic gear used in a laser printer. The impact of these gears measured in foot-pounds is an important characteristic. Assume the impact strength are normally distributed. A random sample of 10 gears from supplier 1 results in = 289.3 and = 22.5. Another sample of 16 gears from supplier 2 result in = 321.5 and = 21. It is claimed that supplier 2 provide gears with higher mean impact strength. Perform the hypothesis test at significance level 0.05.

1. If we assume gear 1 and gear 2 have the same standard deviation, perform the hypothesis test.
2. If we assume gear 1 and gear 2 have different standard deviations, perform the hypothesis test.

Answer 1

SOLUTION-

LET BE THE MEAN IMPACT STRENGTH FOR SUPPLIER-2 AND BE THE MEAN IMPACT STRENGTH FOR SUPPLIER-1. WE WANT TO TEST IF SUPPLIER 2 PROVIDES HIGHER MEAN IMPACT STRENGTH. SO THE HYPOTHESIS IS,

WE PERFORM A TWO SAMPLE-T TEST AS THE SAMPLES ARE INDEPENDENT. WE USE MINITAB-16 TO TEST THE GIVEN HYPOTHESIS,

A.) IF BOTH THE SAMPLES HAVE SAME STANDARD DEVIATION-

STEPS- STAT> BASIC STATISTICS> TWO SAMPLE-T> ENTER THE SUMMARIZED DATA( ENTER THE DATA FOR SUPPLIER_2 AS SAMPLE 1)> ASSUME EQUAL VARIANCES> UNDER 'OPTIONS', SET THE CONFIDENCE LEVEL AS 95.0 AND ALTERNATE AS 'GREATER THAN'> OK

OBSERVATIONS-

THE TEST STATISTIC IS T=3.70 AND THE CORRESPONDING P-VALUE IS 0.001

AS P-VALUE< LEVEL OF SIGNIFICANCE, WE REJECT THE NULL HYPOTHESIS AND CONCLUDE THAT THE MEAN STRENGTH FOR SAMPLE 2 IS HIGHER.

B.) IF BOTH THE SAMPLES HAVE DIFFERENT STANDARD DEVIATION-

STEPS- STAT> BASIC STATISTICS> TWO SAMPLE-T> ENTER THE SUMMARIZED DATA( ENTER THE DATA FOR SUPPLIER_2 AS SAMPLE 1)> DO NOT ASSUME EQUAL VARIANCES> UNDER 'OPTIONS', SET THE CONFIDENCE LEVEL AS 95.0 AND ALTERNATE AS 'GREATER THAN'> OK

OBSERVATIONS-

THE TEST STATISTIC IS T=3.64 AND THE CORRESPONDING P-VALUE IS 0.001

AS P-VALUE< LEVEL OF SIGNIFICANCE, WE REJECT THE NULL HYPOTHESIS AND CONCLUDE THAT THE MEAN STRENGTH FOR SAMPLE 2 IS HIGHER

**** IN CASE OF DOUBT, COMMENT BELOW. ALSO LIKE THE SOLUTION, IF POSSIBLE.