# Testing of Hypothesis

The researcher is similar to the prosecuting attorney is the sense that the researcher brings the null hypothesis “to trial” when she believes there is probability strong evidence against the null.

• Just as the prosecutor usually believes that the person on trial is not innocent, the researcher usually believes that the null hypothesis is not true.
• In the court system the jury must assume (by law) that the person is innocent until the evidence clearly calls this assumption into question; analogously, in hypothesis testing the researcher must assume (in order to use hypothesis testing) that the null hypothesis is true until the evidence calls this assumption into question.

# Specifying the Null and Alternative Hypothesis

## 1) The t-test for independent samples, 2) One-way analysis of variance, 3) The t-test for correlation coefficients?, 4) The t-test for a regression coefficient.

[latexpage]

In each of these, the null hypothesis says there is no relationship and the alternative hypothesis says that there is a relationship.

1. In this case the null hypothesis says that the two population means (i.e., $\mu_1$ and  $\mu_2$) are equal; the alternative hypothesis says that they are not equal.
2. In this case the null hypothesis says that all of the population means are equal; the alternative hypothesis says that at least two of the means are not equal.
3. In this case the null hypothesis says that the population correlation (i.e., $\rho$) is zero; the alternative hypothesis says that it is not equal to zero.
4. In this case the null hypothesis says that the population regression coefficient ($\beta$) is zero, and the alternative says that it is not equal to zero.