Question

A machinist is making engine parts with axle diameters of 0.700 inch. A random sample of 10 parts shows a mean diameter of 0.742 inch with a S.D. of 0.040 inch. Compute the statistic you would use to test whether the work is meeting the specification.

Answer 1

The following null and alternative hypotheses need to be tested:

$H_0:\mu=0.700$

$H_1:\mu\not=0.700$

This corresponds to a two-tailed test, for which a t-test for one mean, with unknown population standard deviation, using the sample standard deviation, will be used.

The t-statistic is computed as follows:

$$t=\dfrac{\bar{x}-\mu}{s/\sqrt{n}}=\dfrac{0.742-0.700}{0.040/\sqrt{10}}\approx3.3204$$