Save
An online poll asked: "Do you believe the Loch Ness monster exists?" Among 21,111 responses, $64 \%$ were "yes. " Use a 0.10 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 test statistic for this hypothesis test.
The test statistic for this hypothesis test is (Round to two decimal places as needed.)

Step 1 ：State the null hypothesis and the alternative hypothesis. The null hypothesis is that the proportion of people who believe in the Loch Ness monster is 0.5 (or 50%). The alternative hypothesis is that the proportion is greater than 0.5.

Step 2 ：The test statistic for a hypothesis test for a proportion is a z-score, which is calculated as \((p̂ - p0) / \sqrt{(p0 * (1 - p0)) / n}\), where \(p̂\) is the sample proportion, \(p0\) is the hypothesized population proportion, and \(n\) is the sample size.

Step 3 ：In this case, \(p̂ = 0.64\), \(p0 = 0.5\), and \(n = 21111\).

Step 4 ：Substitute the values into the z-score formula to get \(z = (0.64 - 0.5) / \sqrt{(0.5 * (1 - 0.5)) / 21111}\)

Step 5 ：Solve the equation to get the z-score.

Step 6 ：Final Answer: The test statistic for this hypothesis test is \(\boxed{40.68}\).