Question

An online poll​ asked: "Do you believe the Loch Ness monster​ exists?" Among 20 comma 385 ​responses, 67​% 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?

A)The test statistic for this hypothesis is:

b) p-value

c)conclusion:

Answer 1

Here the given sample the sample size is 20,385 and the sample proportion which is affirmative in nature is

Now the Hypotheses are:

Ho: p=0.50

Ha: p>0.50

a) The test hypothesis is calculated as

b) The P-value at the Test statistic calculated is almost 0.

c) Conclusion:

Since the Z >>> Z (0.1)=1.28 and P-value <<<0.1 hence we can comfortably say that the we can reject the null hypothesis and conclude that there is enough evidence to supprt the claim.

The Z table: