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Sample Assumption

Runout obtained for 38 gears laid and 39 gears hung after heat treating. Mean laid runout=12.6, Mean hung runout=17.9

Gears laid- 5,8,8,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,15,15,15,15,16,17,17,18,19,27

Gears hung-
7,8,8,10,10,10,10,11,11,11,12,13,13,13,15,17,17,17,17, 18,19,19,20,21,21,21,22,22,22,23,23,23,23,24,27,27,28, 31,36

Use the stepwise significance testing format to assess the strength of the evidence collected in this study to the effect that laying method is different to the hanging method in terms of mean runouts produced.

(a) Under large sample assumption
(b) Under small sample assumption and the two underlying variances are the same

Solution Preview

This is a test of mean difference:
Ho: M2 = M1 or M2-M1 = 0
Ha: M2 ≠ M1 or M2-M1 ≠ 0
where Md=Xno-Xm = 17.95-12.63 = 5.32 (this is a point estimate for the difference between means)
We need to compute the standard error of the difference between means, Smd.

The calculations are complicated when the sample sizes are different (n1 does not equal n2). From the attached EXCEL, we calculate ...

Solution Summary

Runout obtained for 38 gears laid and 39 gears hung after heat treating. Mean laid runout=12.6, Mean hung runout=17.9

Gears laid- 5,8,8,9,9,9,9,10,10,10,11,11,11,11,11,11,11,12,12,12,12,13,13,13,13,14,14,14,15,15,15,15,16,17,17,18,19,27

Gears hung-
7,8,8,10,10,10,10,11,11,11,12,13,13,13,15,17,17,17,17, 18,19,19,20,21,21,21,22,22,22,23,23,23,23,24,27,27,28, 31,36

Use the stepwise significance testing format to assess the strength of the evidence collected in this study to the effect that laying method is different to the hanging method in terms of mean runouts produced.

(a) Under large sample assumption
(b) Under small sample assumption and the two underlying variances are the same

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