An online poll asked: "Do you believe the Loch Ness monster exists?" Among 21,470 responses, $63 \%$ were "yes." Use a 0.01 significance level to test the claim that most people believe that the Loch Ness monster exists. How is the conclusion affected by the fact that Internet users who saw the question could decide whether to respond? Identify the null and alternative hypotheses for this test. Choose the correct answer below. A. \[ \begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p<0.5 \end{array} \] B. \[ \begin{array}{l} H_{0}: p>0.5 \\ H_{1}: p=0.5 \end{array} \] C. \[ \begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p \neq 0.5 \end{array} \] 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 38.10 . (Round to two decimal places as needed.) Identify the P-value for this hypothesis test. The $P$-value for this hypothesis test is (Round to three decimal places as needed.) Clear all Check answer
Solution
Step 1 ：First, we need to identify the null and alternative hypotheses for this test. The null hypothesis, denoted by \(H_{0}\), is a statement of no effect or no difference. The alternative hypothesis, denoted by \(H_{1}\), is a statement that indicates the presence of an effect or difference. In this case, we are testing the claim that most people believe that the Loch Ness monster exists. Therefore, the null hypothesis is that the proportion of people who believe in the Loch Ness monster is equal to 0.5, and the alternative hypothesis is that the proportion is greater than 0.5. So, the correct answer is D: \[\begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p>0.5 \end{array}\]
Step 2 ：Next, we need to identify the test statistic for this hypothesis test. The test statistic is a measure of how far our sample statistic is from the null hypothesis value, measured in standard errors. In this case, the test statistic is given as 38.10.
Step 3 ：Finally, we need to identify the P-value for this hypothesis test. The P-value is the probability of obtaining a result as extreme as, or more extreme than, the observed data, assuming that the null hypothesis is true. In this case, the P-value is not given, so we cannot determine it from the information provided.
