Question

An online poll asked:"Do you believe the Loch Ness monster exists?" Among 21,213 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 the internet users who saw the question could decide whether to respond?

identify the test statistic for this hypothesis test?

identify the P-Value?

identify the conclusion?

Answer 1

null Hypothesis:              Ho:   p=		0.500
alternate Hypothesis:    Ha: p >		0.500

sample size          n    =		21213
std error σp =√(p*(1-p)/n) =		0.0034
sample prop p̂ = x/n=13576.32/21213=		0.6400
z =(p̂-p)/σp=(0.64-0.5)/0.64=		40.78
p value                          =		0.0000	(from excel:1*normsdist(-40.7811)

Conclusion: reject Ho, we have sufficient evidence at 0.01 level to support the claim that most people believe that the Loch Ness monster exists