Question

An online poll​ asked: "Do you believe the Loch Ness monster​ exists?" Among 20, 404 ​responses, 63% were​ "yes." Use a 0.05 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?

The null and alternative hypotheses for this test is:

H0​: p=0.5

H1​: p>0.5

Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is____.​(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.)

Identify the conclusion for this hypothesis test.

A. Fail to reject H0. There is sufficient evidence to warrant rejection of the claim that most people believe that the Loch Ness monster exists.

B. Fail to reject H0. There is not sufficient evidence to warrant rejection of the claim that most people believe that the Loch Ness monster exists.

C. Reject H0. There is not sufficient evidence to warrant rejection of the claim that most people believe that the Loch Ness monster exists.

D. Reject H0. There is sufficient evidence to support the claim that most people believe that the Loch Ness monster exists.This is the correct answer.

How is the conclusion affected by the fact that Internet users who saw the question could decide whether to​ respond?

A. Since only certain users are being allowed to​ respond, the conclusion is not valid.

B. Since the sample size is sufficiently​ large, the conclusion is valid.

C. Since the sample is a​ voluntary-response sample, the conclusion might not be valid.

D. Since any of the​ site's users are allowed to​ respond, the conclusion is valid.

Answer 1

Test statistics for hypothesis is calculated as follows:

Test statistics z = (p - p₀)/SQRT((p₀*(1-p₀)/n))

Here, p = Sample proportion, p₀ = Null hypothesis value = 0.5, and n = 20404

Test statistics z = (0.63 - 0.50)/SQRT((0.5*(1-0.5)/20404))

Test statistics z = 37.146

The test statistic for this hypothesis test is 37.15

P-value calculation

We have to find out p-value corresponding to z = 37.15 for one tailed test

p-value = 0.000 (Very small) (Obtained using online p-value calculator)

The​ P-value for this hypothesis test is 0.000

Conclusion for this hypothesis test

In this case, p-value is less than 0.05 level of significance, so we reject null hypothesis. There is sufficient evidence to support the claim that most people believe that the Loch Ness monster exists (Option D is correct).

Conclusion affected by the fact that Internet users

One of the conditions needed for inference on one proportion is that the data needs to come from a random sample or randomized experiment. However in this case, since only certain users are being allowed to​ respond, the conclusion is not valid (Option A is correct)