Hypothesis Testing Problems – Question 8(An automatic cutter machine…)

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

H₀: μ₀ = μ₁
H_a: μ₀ ≠ μ₁

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