Question

A company produces thousands of plastic toy parts every day. So that the toys can be assembled properly a certain tab thickness x has to meet quality control specifications. The mean of the population of x has to be within a certain range and the standard deviation of the population of x has to be less than a certain value. A quality control inspector took a random sample of 18 parts and measured x. He computed a sample mean of 8.2 mm for x and a sample standard deviation of 0.024 mm.

Having found the mean was in spec next he has to test the sample variance to decide whether to reject the null hypothesis that the population variance of x is less than or equal to the quality tolerance 0.0002 mm^2 using alpha of 0.05. He assumes the population mean follows a normal distribution. Do this test by answering the following questions.

1) what diagram would show the reject/fail to reject region for this problem?

2) what is the test statistic is used for question 1?

3) what is the teste statistic value computed from the sample statistic given in question 1?

4) since the level of significance alpha is 0.05 state the critical value which you would use relevant to question 1. also state your conclusion about the null hypothesis based on question 1-3.

Answer 1