- to illustrate a hypothesis testing procedure for a mean
- to show how the Student t distribution is used in a hypothesis test
- to show how to use hand calculations in a hypothesis testing procedure
Hypothesis testing is a very strange statistical process - we take a lot of time getting accustomed to what it is and to the logic behind it. This example should take away some of the mystery!
Just remember that a hypothesis test is just another way to think of a confidence interval - if you get confidence intervals, then hypothesis tests are not that difficult. So, go back to the section on confidence intervals and review that if you are having a lot of difficulty with the idea of hypothesis testing.
Part 1 gives the set-up to the problem. We will figure out what the Claim, Null and Alternative hypotheses are. Then, we will settle on the correct distribution and see where the critical region is.
In the second part we calculate the test statistic and determine the critical value.
We finish off this example by giving "regular language" wording to the final conclusion - it is important to do this so that an average person looking at your results will know what you mean by your conclusion.
The manufacturer is concerned with establishing the validity of the claim that the light bulbs last at least as long as 250 hours - so the claim is stated as such.
The consumer is concerned with faulty light bulbs - those that do not meet the manufacturer's stated burnout time - and so will state the claim to reflect that concern - bulbs last for a shorter time than the manufacturer says they do.