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t-Test (Assuming Equal and Unequal Variances)

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A company making plastic opitical components for bar code scanners was studying inconsistencies in an optical measurement called tilt. The company knew that scanners work best when tilt measurement is small. Two different types of locking mechanisms used in the mold produced the following units.

Taper Locks Locking Pins
X= 1.262 0.561

S 0.297 0.307

n 20 20

a Assuming that the population variances are equal and the populations are normally distributed, at the 0.05 level of significance is there evidence of a difference in the means between taper locks and locking pins.

b. Repeat (a) assuming that the population variances are not equal.

c. compare the results of a and b

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Solution Summary

The solution also provides step-by-step method of performing a two-tailed hypothesis t-test assuming both equal and unequal variances. All the steps of hypothesis testing (formulation of null and alternate hypotheses, selection of significance level, choosing the appropriate test-statistic, decision rule, calculation of test-statistic and conclusion) have been explained and the statistical analysis has been shown in details.

Solution provided by:
Anwesha Ghosh, MSc
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  • MSc, Osmania University
  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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