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: \[\boxed{\begin{array}{l} H_{0}: p=0.5 \\ H_{1}: p>0.5 \end{array}}\]