8.1. Hypothesis Testing and the P-Value http://www.ck12.org
In statistics, the hypothesis to be tested is called thenull hypothesisand given the symbolH 0. The null hypothesis
states that there is no relationship or no difference between an accepted population mean and a sample mean. So
finding a significant result means refuting the null hypothesis, showing that the true population mean is likely to be
closer to the sample mean. We would calculate the mean of the sample and generalize these findings to the overall
population. For example, if we were to test the hypothesis that the seniors had a mean SAT score of 1, 100 ,our null
hypothesis would be that the SAT score would be equal to 1,100 or:
H 0 :μ= 1100where:
H 0 =symbol for null hypothesis
μ=population mean
1 , 100 =value to be tested
We test the null hypothesis against analternative hypothesis,which is given the symbolHaand includes the
outcomes not covered by the null hypothesis. Basically, the alternative hypothesis states that there is a difference
between the hypothesized population mean and the sample mean. The alternative hypothesis can be supported only
by rejecting the null hypothesis. In our example above about the SAT scores of graduating seniors, our alternative
hypothesis would state that there is a difference between the null and alternative hypotheses or:
Ha:μ 6 = 1100Let’s take a look at a couple of examples and develop a few null and alternative hypotheses.
Example:
We have a medicine that is being manufactured and each pill is supposed to have 14 milligrams of the active
ingredient. What are our null and alternative hypotheses?
Solution:
H 0 :μ= 14
Ha:μ 6 = 14Our null hypothesis states that the population has a mean equal to 14 milligrams.Our alternative hypothesis states
that the population has a mean that is different than 14 milligrams.
Example:
The school principal wants to test if it is true what teachers say – that high school juniors use the computer an average
3 .2 hours a day. What are our null and alternative hypotheses?