**Math 221 – Principles of
Statistics**

**
Hypothesis Tests: An Outline**

An hypothesis is a claim about a parameter. (Recall that a parameter is a measure of some characteristic of a population.) Usually, hypotheses arise from consideration of theory or anecdotal evidence, or in response to other research.

1) We need two hypotheses for each test. One of them represents “no change,” “no
difference,” “no effect,” or something similar. It is called the *
null hypothesis*,
and can be thought of as
“what to expect if things are the way we
think they are (or have been).” The other
hypothesis represents some alternative to the null hypothesis, (some alternative
expectation) and so is called
the *alternative hypothesis*.

2) We establish the standard by which the significance (or lack thereof) of our
experimental results will be judged. This standard is the *
significance level* of the test. Its
default value is 5% = 0.05, but is typically as low as 1% = 0.01 or as high as
10% = 0.10. Its symbol is the Greek letter
.

3) We design the study, describing very carefully the population being studied, the design of the experiment, the sampling method to be used, the measurements we will make and how to make them, organization and training of the research team, etc.

4) We take the sample and measure, keeping very careful records of what we’ve done and the data we’ve obtained.

5) We summarize the data with appropriate descriptive statistics and graphics. Example: , histogram, etc.

6)
a) We compute the *test statistic*.
This is a standardized value of a sample statistic.

Example:

b) We use
the test statistic to determine how likely it was that we should
have gotten the result we got, __ assuming the null hypothesis (the
expectation) is true__. This
likelihood is called the

7) We compare the P-value with the significance level alpha. If the P-value
,
our statistic is __contrary to expectation.__ We say the result is "statistically significant (at the
level)" and reject the null hypothesis. If the P-value
,
our statistic is __consistent with our expectation__. We say the result is "not statistically significant" and fail to reject the null hypothesis.

8) We interpret our results for appropriate audiences.

Note: In the homework, you will typically carry out only steps 1, 6, 7 and 8. On rare occasions, you may carry out steps 2 and 5. But the homework in this text will not require you to carry out steps 3 and 4. Frankly, you need to learn a lot more before you can do step 3 (no offense) and step 4 requires resources we simply don't have.

BYU-Idaho mailto:brownd@byui.edu

232 Ricks Building 208-496-1839 voice

Rexburg, ID 83440 208-496-2005 fax

**Please
do not call me at home.**