Question

1. A product is produced on a particular workbench of a factory. The quality characteristic of the product follows Normal distribution with an average of 3 mm and a standard deviation of 0.1 mm. In order to test whether the bench is working properly, 15 random samples were taken and the average was found to be 2.94 mm. Test whether the workbench is working properly at the 0.05 significance level.

Answer 1

Solution:

Since sample size n is less than 30 we use a t-test for determining the significance.

$t = \frac{X-\mu}{\frac{\sigma}{\sqrt{n}}}$

$t = \frac{2.94-3}{\frac{0.1}{\sqrt{15}}}$

We refer to the t table values,

Hence, the critical value of reference for a degree of freedom of 14 and a significance level of 0.05 is 1.771

Since the t-statistic is more than the critical value of reference we reject the null hypothesis.

The result of the sample is hence significant for a significance level of 0.05.