Question

A company manufactures components for laptop PC's. The company performs a "torture test" to see how long a certain component (which usually only runs for a few seconds at a time) can operate continuously until it fails.

They test a sample of 8 components manufactured by their company and the failure times (in hours) are:

270, 310, 316, 280, 295, 301, 335, 284

The company then tests a sample of six of these components made by a computer and the failure times in hours are:

315, 330, 328, 307, 295, 342

Assume that the failure rate times in both groups are normally distributed, and also assume that we could reasonably believe that either company's product is potentially superior to the other's.

The mean failure time for the company's component was: ______________ hours

The mean failure time for the competitor's component was: ______________ hours

The p-value of the hypothesis test is: ___________

Answer 1

Mean failure time for company's component

sample variance for companys's component

Mean failure time for company's competitor's component

sample variance for companys's competitor's component

Since it is a two-sample t test with EQUAL VARIANCE, the the test-statistic for this test is given as-

where, pooled variance

So, the test-statistic is calculated as

P-value:

Since it is a one-tailed test, so the p-value is given as-

The p-value is calculated as