**Question**

An automatic cutter machine must cut steel strips of 1200 mm lenght. From a preliminary data, we checked that the lenghts of the pieces produced by the machine can be considered as normal random variables with a 3mm standard deviation. We want to make sure that the machine is set currectly. Therefore 16 pieces of the products are randomly selected and weight. The figures were in mm:

1193,1196,1198,1195,1198,1199,1204,1193,1203,1201,1196,1200,1191,1196,1198,1191

Examine wether there is any significant deviation from the required size

**Solution Steps**

As usual, try to understand the question so we can choose a test to use. From the question:

- the standard deviation of the sample is given
- the population is said to be normally distributed

So we can safely use one-sample t-test

Let’s follow the six easy steps of performing z-test.

Note: Some texts refer to this test as u-test

**Step 1:** State the null and the alternate hypothesis

**H _{0}:** μ

_{0}= μ

_{1}

**H**: μ

_{a}_{0}≠ μ

_{1}

**Step 2:** Calculate the mean of the sample

Mean = 1197

**Step 3: **Calculate the test statistic

This is gotten using the formula and the steps

**Step 4:** Look up value of z from the statistical table and compare with the calculated value

From the table of z statistic we look up the critical value of z for 15 degrees of freedom and 0.05 significance

Statistical table here

This give us 0.0975

**Step 5:** Draw a conclution

Since the calculated value of z is greater than the critical value, we reject the null hypothesis