# A machine produces 3-inch nails

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 *H*_{0}: *m* = 3 and *H*_{a}: *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 deviation_{}is 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.

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