A machine produces 3-inch nails. A sample of 10 nails was selected and the lengths determined. The results are as follows:

2.89 2.95 3.00 3.05 2.99 2.96 3.10 3.06 3.00 3.12

Use these results to test H0: m = 3 and Ha: m ¹ 3 at a = 0.01. Give the critical region, the computed test statistic, and the conclusion.

Solution: From the sample we get that

Solution: We want to test following null and alternative hypotheses

Since the population standard deviationis unknown, we are can use a t-test. In fact, we’ll use a two-tailed t-test. The t-statistics is given by the following formula:

The two-tailed critical t-value for and degrees of freedom is equal to

Since we have that, we fail to reject the null hypothesis. This means that we don’t have enough evidence to support the claim that the mean is different from 3, at the significance level.