Question

It is important that the mean response from a manufacturing process be increased, but any change to the process is expensive to implement. A team listed some changes that they thought would be beneficial. They conducted a test with the current process settings and the new settings. They wanted to be certain that the change would be beneficial before implementing it. For this reason, they decided to keep the current process unless they could prove that the new process would be beneficial at a level of significance of 0.01. Discuss results and assess what should be done.

Current process readings: 98.1, 102.3, 98.5, 101.6, 97.7, 100.0, 103.1, 99.1, 97.7, 98.5

New process readings: 100.9, 101.1, 103.4, 85.0, 103.4, 103.6, 100.0, 99.7, 106.4, 101.2

Answer 1

Let us denote :

d = New process readings - Current process readings

To test against

Here

sample mean of difference

sample standard deviation of difference

and sample size

The test statistic can be written as

which under H₀ follows a t distribution with n-1 df.

We reject H₀ at 0.05 level of significance if P-value < 0.05

Now,

The value of the test statistic =

P-value =

Since P-value > 0.05, so we fail to reject H₀ at 0.05 level of significance and we can conclude that mean response has not increased significantly by the new process.