# How to Set Up a Hypothesis Test: Null versus Alternative

Accepting the does not mean that it is true. It is still a hypothesis, and must conform to the principle of , in the same way that rejecting the null does not prove the alternative.

## One can never prove the truth of a statistical (null) hypothesis.

### rejecting the null hypothesis when the alternative is true.

Simple logistic regression finds the equation that best predicts the value of the *Y* variable for each value of the *X* variable. What makes logistic regression different from linear regression is that you do not measure the *Y* variable directly; it is instead the probability of obtaining a particular value of a nominal variable. For the spider example, the values of the nominal variable are "spiders present" and "spiders absent." The *Y* variable used in logistic regression would then be the probability of spiders being present on a beach. This probability could take values from 0 to 1. The limited range of this probability would present problems if used directly in a regression, so the odds, *Y*/(1-*Y*), is used instead. (If the probability of spiders on a beach is 0.25, the odds of having spiders are 0.25/(1-0.25)=1/3. In gambling terms, this would be expressed as "3 to 1 odds *against* having spiders on a beach.") Taking the natural log of the odds makes the variable more suitable for a regression, so the result of a logistic regression is an equation that looks like this:

### not rejecting the null hypothesis when the alternative is true.

In the output above, Minitab reports that the *P*-value is 0.158. Since the *P*-value, 0.158, is greater than α = 0.05, the quality control specialist fails to reject the null hypothesis. There is insufficient evidence, at the α = 0.05 level, to conclude that the mean thickness of all pieces of spearmint gum differs from 7.5 one-hundredths of an inch.

## Civil Essay: Simple Null Hypothesis Example free …

The major problem with the H_{0} is that many researchers, and reviewers, see accepting the null as a failure of the . This is very poor science, as accepting or rejecting any hypothesis is a positive result.

## A Null Hypothesis for the New Year | Flirting with Models

If the biologist used the *P*-value approach to conduct her hypothesis test, she would determine the area under a *t*_{} = *t*_{} curve and to the *left *of the test statistic * t** = -4.60:

## Simple hypotheses only test against one value of the ..

In the output above, Minitab reports that the *P*-value is 0.000, which we take to mean *P*-value is less than 0.001, it is clearly less than α = 0.05, and the biologist rejects the null hypothesis. There is sufficient evidence, at the α = 0.05 level, to conclude that the mean height of all such sunflower seedlings is less than 15.7 cm.