- Perform a test for significance of slope and interpret the results
- Check the conditions that are necessary to perform a test for significance of slope
- Write out the null and alternative hypotheses.
- Null Hypothesis: [latex]\beta_1 = 0[/latex]
- Alternative Hypothesis: [latex]\beta_1 \ne 0[/latex]
- Check the conditions for the hypothesis test. For testing a one-sample z-test for proportions, we require:
- A random sample of data
- A linear trend
- No obvious trends in the residual plot
- Calculate the test statistic: [latex]t=\dfrac{b-0}{[\text{std. error of }b]} = \dfrac{b}{SE_b}[/latex]
- Calculate a P-value.
- Compare the P-value to the significance level, [latex]\alpha[/latex], to make a decision.
Decision Conclusion If P-value [latex]\le\alpha[/latex], there is enough evidence to reject the null hypothesis. At the [latex]\alpha\times[/latex]100% significance level, the data provide convincing evidence in support of the alternative hypothesis. If P-value [latex]\gt\alpha[/latex], there is not enough evidence to reject the null hypothesis. At the [latex]\alpha\times[/latex]100% significance level, the data do not provide convincing evidence in support of the alternative hypothesis. - Write a conclusion in context (e.g., we do/do not have convincing evidence…).