  ## Summary of the 3 Approaches to Hypothesis Testing

#### Steps to Conduct a Hypothesis Test Using $p$-values:

1. Identify the null hypothesis and the alternative hypothesis (and decide which is the claim).

2. Ensure any necessary assumptions are met for the test to be conducted.

3. Find the test statistic.

4. Find the p-value associated with the test statistic as it relates to the alternative hypothesis.

5. Compare the p-value with the significance level, $\alpha$. If $p \lt \alpha$, conclude that the null hypothesis should be rejected based on what we saw. If not, conclude that we fail to reject the null hypothesis as a result of what we saw.

6. Make an inference.

#### Steps to Conduct a Hypothesis Test Using Critical Values:

1. Identify the null hypothesis and the alternative hypothesis (and decide which is the claim).

2. Ensure any necessary assumptions are met for the test to be conducted.

3. Find the test statistic.

4. Find the critical values associated with the significance level, $\alpha$, and the alternative hypothesis to establish the rejection region in the distribution.

5. If the test statistic falls in the rejection region, conclude that the null hypothesis should be rejected based on what we saw. If not, conclude that we fail to reject the null hypothesis as a result of what we saw.

6. Make an inference.

#### Steps to Conduct a Hypothesis Test Using a Confidence Interval:

1. Identify the null hypothesis and the alternative hypothesis (and decide which is the claim).

2. Ensure any necessary assumptions are met for the test to be conducted.

3. Construct a confidence interval with a confidence level of $(1-\alpha)$

4. If the hypothesized population parameter falls outside of the confidence interval, conclude that the null hypothesis should be rejected based on what we saw. If it falls within the confidence interval, conclude that we fail to reject the null hypothesis as a result of what we saw.

5. Make an inference.