Part 2 of 5
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 (Round to two decimal places as needed.)
Clear all
Check answer

Step 1 ：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 people who believe in the Loch Ness monster is equal to 0.5 (or 50%), which is the threshold for 'most people'.

Step 2 ：The alternative hypothesis (H1) is what we are testing against the null hypothesis. In this case, we are testing the claim that most people believe in the Loch Ness monster, which would mean that the proportion is greater than 0.5.

Step 3 ：So, the correct hypotheses would be: \[H_{0}: p=0.5\] \[H_{1}: p>0.5\]

Step 4 ：The test statistic for this hypothesis test can be calculated using the formula for a one-sample z-test for proportions, which is \((p̂ - p0) / \sqrt{(p0 * (1 - p0)) / n}\), where p̂ is the sample proportion, p0 is the proportion under the null hypothesis, and n is the sample size.

Step 5 ：In this case, p̂ = 0.63, p0 = 0.5, and n = 21470.

Step 6 ：Substituting these values into the formula, we get a test statistic of approximately 38.10.

Step 7 ：Final Answer: The null and alternative hypotheses for this test are: \[H_{0}: p=0.5\] \[H_{1}: p>0.5\] The test statistic for this hypothesis test is \(\boxed{38.10}\).