# A small (p)-valueis an indication that the null hypothesis is false.

This number, 0.030, is the *P* value. It is defined as the probability of getting the observed result, or a more extreme result, if the null hypothesis is true. So "*P*=0.030" is a shorthand way of saying "The probability of getting 17 or fewer male chickens out of 48 total chickens, *IF* the null hypothesis is true that 50% of chickens are male, is 0.030."

## Five Steps in a Hypothesis Test

### What a p-Value Tells You about Statistical Data

Lastly, we need to set the "alpha value" which can be viewed as a "threshold for acceptance." Common values are .05, .01, and .001. With an alpha value of .05, there is a 95% chance your results are correct. With a value of .01, there is a 99% chance your results are correct, and so on. . . You can never have an alpha value of zero, because you can never be 100% confident of anything in statistics (this is not a joke).

### Null and Alternative Hypotheses for a Mean

The good news is that, whenever possible, we will take advantage of the test statistics and *P*-values reported in statistical software, such as Minitab, to conduct our hypothesis tests in this course.

## Use the following formula to calculate your test value.

Before we can begin to crunch some numbers, we must clearly define our null and alternative hypothesis. You may be asking why we need two hypotheses for a statistical test. In formal statistics, we always compare two hypotheses, the null and alternative.

## Since the p-value ll hypothesis with an alpha value of 0.05.

The p-value is the probability that a t-value would be greater than (to the right of ) 4.03. From Minitab we get 0.001. If using we would look at DF = 9 and since t = 4.03 > 3.00 our p-value from the table would p

## Use the following formula to calculate your test value.

The T-test is powerful, because it allows us to make inferences from a small sample size about the whole population. We will show you how to do a T-test for the first hypothesis, but it will be up to you to perform the T-test for the second hypothesis.