Question
Asked Feb 18, 2020
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Is Nessie Real? This question was posted on the America Online website: Do you believe the Loch Ness monster exists? Among 21,346 responses, 64% 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?

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Expert Answer

Step 1

Formation of Hypothesis

Null hypothesis:

 H0p=0.5.

That is, the percentage of people who believe that the Loch Ness monster exists is equal to 50%.

Alternative hypothesis:

 H1p>0.5.

That is, the percentage of people who believe that the Loch Ness monster exists is greater than 50%.

From the given information, there are 21,346 responses and 64% of people who believe that the Loch Ness monster exists.

That is, the sample size is, n =21,346 and the sample proportion is   =0.64(=64%).

Test statistic is given by 

Statistics homework question answer, step 1, image 1

 

Step 2

p-value is given by 

p-value = P(Z > Z test)

              = P( z > 40.908)

               = (1 – 1) = 0 [From Excel = NORM.DIST(40.908,0,1,TRUE)

Step 3

Decision Rule:

 

If P-value ≤ α, then reject the null hypothesis.

If P-value > α, then do not reject the null hypothesis.

 

 

Conclusion:

 

From the given information, the level of significance is α=0.01

The P-value is 0.000.

Here, the P-value is lesser than the level of significance.

That is, P(=0.0...

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