k: Homework Chapter 8
Question 17, 8.2.29-T
HW Score: $57.14 \%, 16$ of 28 points
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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
Answer
Final Answer: \[\boxed{\begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p>0.5 \end{array}}\]
Step 1 ：The first question is asking to identify the null and alternative hypotheses for this test. The null hypothesis is usually a statement of no effect or no difference. The alternative hypothesis is what you might believe to be true or hope to prove true.
Step 2 ：In this case, we are testing the claim that most people believe that the Loch Ness monster exists. 'Most' implies more than 50%, so the null hypothesis should be that the proportion of people who believe in the Loch Ness monster is equal to 50% (p=0.5). The alternative hypothesis should be that the proportion is greater than 50% (p>0.5).
Step 3 ：So, the correct answer should be: \[\begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p>0.5 \end{array}\]
Step 4 ：Final Answer: \[\boxed{\begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p>0.5 \end{array}}\]
