Write the null and alternative hypotheses for each of the following
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.
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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.
