**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.

*t*-test for independent samples,

*t*-test for a regression coefficient.

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

- 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.
- 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.
- 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.
- 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.