In one study of smokers who tried to quit smoking with nicotine patch therapy, 39 were smoking one year after treatment and 31 were not smoking one year after the treatment. Use a 0.01 significance level to test the claim that among smokers who try to quit with nicotine patch therapy, the majority are smoking one year after the treatment. Do these results suggest that the nicotine patch therapy is not effective? Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. \[ \begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p \neq 0.5 \end{array} \] B. \[ \begin{array}{l} H_{0}: p>0.5 \\ H_{1}: p=0.5 \end{array} \] C. \[ \begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p<0.5 \end{array} \] D. \[ \begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p>0.5 \end{array} \] Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test is (Round to two decimal places as needed.)

Step 1 ：Identify the null and alternative hypotheses for this test. The null hypothesis (H0) is usually a statement of no effect or no difference. In this case, the null hypothesis would be that the proportion of smokers who are still smoking one year after treatment is equal to 0.5 (or 50%). The alternative hypothesis (H1) is what we are testing against the null hypothesis. In this case, we are testing the claim that the majority of smokers are still smoking one year after treatment, so the alternative hypothesis would be that the proportion of smokers who are still smoking one year after treatment is greater than 0.5. The correct answer is: \[ \begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p>0.5 \end{array} \]

Step 2 ：Identify the test statistic for this hypothesis test. The test statistic for this hypothesis test can be calculated using the formula for the z-score, which is \((p̂ - p0) / \sqrt{(p0 * (1 - p0)) / n}\), where p̂ is the sample proportion, p0 is the hypothesized population proportion in the null hypothesis, and n is the sample size.

Step 3 ：In this case, p̂ is the proportion of smokers who are still smoking one year after treatment, which is 39 / (39 + 31) = 0.557. p0 is the hypothesized population proportion in the null hypothesis, which is 0.5. And n is the sample size, which is 39 + 31 = 70.

Step 4 ：Substitute the values into the z-score formula to get the test statistic: \(z = (0.557 - 0.5) / \sqrt{(0.5 * (1 - 0.5)) / 70} = 0.96\)

Step 5 ：The test statistic for this hypothesis test is \(\boxed{0.96}\)