Suppose you are using the first 100 rows of the Oakland data to test the hypotheses $H_0:p_1=p_2$ versus an alternative hypothesis about $p_1$. Which of the following is the correct first step in the hypothesis testing process?

• A. Calculate the p-value using the sample data.
• B. Interpret the results in the context of the Oakland data.
• C. Draw a conclusion about the null hypothesis based on the test statistic.
• D. Clearly state the null and alternative hypotheses, including the direction of the alternative hypothesis.

Answer: (D)

Verified step by step guidance

1. Begin by clearly stating the null hypothesis \(H_0\) and the alternative hypothesis \(H_a\). For example, \(H_0: p_1 = p_2\) and depending on the research question, specify the alternative hypothesis as either \(H_a: p_1 \neq p_2\), \(H_a: p_1 > p_2\), or \(H_a: p_1 < p_2\) to indicate the direction of the test.
2. Next, identify the appropriate test statistic for comparing two population proportions. This typically involves calculating the difference between the sample proportions and standardizing it using the pooled proportion under the null hypothesis.
3. Then, calculate the test statistic using the sample data from the first 100 rows of the Oakland dataset. This involves computing the sample proportions \(\hat{p}_1\) and \(\hat{p}_2\), the pooled proportion \(\hat{p}\), and then the test statistic formula:
4. \[ Z = \frac{\hat{p}_1 - \hat{p}_2}{\sqrt{\hat{p}(1 - \hat{p}) \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}} \]
5. After obtaining the test statistic, calculate the p-value corresponding to this statistic based on the alternative hypothesis direction. Finally, interpret the p-value in the context of the Oakland data to decide whether to reject or fail to reject the null hypothesis.