# 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. 