Hypothesis Test - Mean

Hypothesis Test - Mean

Author: mary daunis

- 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.

See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to over 2,000 colleges and universities.*

Begin Free Trial
No credit card required

27 Sophia partners guarantee credit transfer.

245 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 21 of Sophia’s online courses. More than 2,000 colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.


Mean - Part 1

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.

Mean - Part 2

In the second part we calculate the test statistic and determine the critical value.

Mean - Part 3

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.

Another Look at the Light Bulb Claim - Manufacturer's Perspective

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.

Another Look at the Light Bulb Claim - Consumer's Perspective

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.