John’s Limited manufactures screws that are used in the manufacture of tables. The table manufacturers require that the screws must have a length of 150 mm, with a small tolerance for differences in length. Resultantly, John’s Ltd randomly sampled and measured the average length of screws for 25 production runs. Due to the fact that the table manufacturers require a small tolerance for differences in the length of the screws, a 1% significance level for evaluation was chosen.

After measuring the average of the samples and their standard deviation, it was observed that the sample values was normally distributed about the mean.
Assume John’s Ltd derived the following values from their test:

Mean = 150.12
Standard Deviation = 0.496

Requirements:
Consider the above scenario and conduct a hypothesis test using the 1% significance. In your answer, include the different steps used to construct a hypothesis test using the critical value method. See steps below.

•Null and alternative hypotheses

•Level of significance

•Test statistics

•Critical values and rejection region

•Process of checking to see whether the test statistic falls in the rejection region and conclusion in words