Question

An online poll​ asked: "Do you believe the Loch Ness monster​ exists?" Among

20 comma 62220,622

​responses,

6767​%

were​ "yes." Use a

0.050.05

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?

Identify the null and alternative hypotheses for this test. Choose the correct answer below.

A.

Upper H 0H0​:

pequals=0.50.5

Upper H 1H1​:

pnot equals≠0.50.5

Your answer is not correct.

B.

Upper H 0H0​:

pequals=0.50.5

Upper H 1H1​:

pless than<0.50.5

C.

Upper H 0H0​:

pequals=0.50.5

Upper H 1H1​:

pgreater than>0.50.5

This is the correct answer.

D.

Upper H 0H0​:

pgreater than>0.50.5

Upper H 1H1​:

pequals=0.50.5

Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is

nothing.

​(Round to two decimal places as​ needed.)

Answer 1

Solution :

Null and alternative hypotheses :

The null and alternative hypotheses would be as follows :

H_{​​​​​​0} : p = 0.5

H_{​​​​​​1} : p > 0.5

Test statistic :

To test the hypothesis the most appropriate test is one sample z-test for proportion. The test statistic is given as follows :

Where, p̂ is sample proportion, p is hypothesized value of population proportion under H_{​​​​​​0}, q = 1 - p and n is sample size.

We have, p̂ = 0.67, p = 0.5, q = 1 - 0.5 = 0.5 and n = 20622

The value of the test statistic is 48.8252.

P-value :

Since, our test is right-tailed test, therefore we shall obtain right-tailed p-value for the test statistic. The right-tailed p-value is given as follows :

P-value = P(Z > value of the test statistic)

P-value = P(Z > 48.8252)

P-value = 0.0000

The p-value is 0.0000.

Decision :

Significance level = 0.05

P-value = 0.0000

(0.0000 < 0.05)

Since, value of the test statisic is less than the significance level of 0.05, therefore we shall reject the null hypothesis (H_{​​​​​​0}) at 0.05 significance level.

Conclusion : At 0.05 significance level, there is sufficient evidence to support the claim that most people believe that the Loch Ness monster exists.