Null Hypothesis in Analysis and Testing

Question

I have my end of year exams next Thursday. I'm generally doing fine but I am having some major issues with this strand of my course, this has to be the biggest issue I have. So, here is the question in the past paper:

You have been tasked with determining the validity of a manufacturer’s claim that their widget is more reliable than their main competitors’ widgets.

In order to verify this assertion you test a sample of 25 widgets from the manufacturer’s range and find a mean pass rate of 992 per 1000 with a standard deviation of 15 per 1000.

Previous studies have shown that the mean pass rate of all other widgets on the market is 979.4 per1000.

In order to increase the confidence in the making a decision about the null hypothesis you choose a 99.5% confidence level and find the corresponding t-table value to be 2.947.

• State the null hypothesis.

I have revision notes in front of me, but I just don't understand what this question is actually asking. Am I just writing down my own hypothesis, or do I need to use this equation?

H0; μ
H1; μ

If anyone could go through step by step for what I need to do, then that would be fantastic. My notes are just confusing!

Answer 1

For your particular problem, the null hypothesis is

$H_0: \mu_{manifacturer} = \mu_{competitors}$

and the alternative hypothesis is

$H_1: \mu_{manifacturer} > \mu_{competitors}$.

Basically, the null hypothesis states that there is no difference between the widget under test and the widgets made by other competitors. The alternative hypothesis states that, instead, there is a difference and the widget under test is better than the widgets made by the competitors.

Now, in your statistical significance test, you are trying to determine if you can reject the null hypothesis, i.e, if the data can be used to demonstrate for a specific confidence level that the widget made by this manufacturer may be better than the ones made by the competitors on the market. Note that I wrote "may be". If you can not reject the null hypothesis on the basis of the available data, this is interpreted by saying that statistically the data do not provide enough evidence to support your assumption that the widget under test is better.

See this Wikipedia article and this one on Statistical hypothesis testing for additional information.