Question

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

21 comma 01921,019

​responses,

6161​%

were​ "yes." Use a

0.010.01

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?

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

B.

Upper H 0H0​:

pgreater than>0.50.5

Upper H 1H1​:

pequals=0.50.5

C.

Upper H 0H0​:

pequals=0.50.5

Upper H 1H1​:

pgreater than>0.50.5

D.

Upper H 0H0​:

pequals=0.50.5

Upper H 1H1​:

pless than<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.)

Identify the​ P-value for this hypothesis test.

The​ P-value for this hypothesis test is

nothing.

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

Identify the conclusion for this hypothesis test.

A.

RejectReject

Upper H 0H0.

There

isis

sufficient evidence to support the claim that most people believe that the Loch Ness monster exists.

B.

Fail to rejectFail to reject

Upper H 0H0.

There

isis

sufficient evidence to warrant rejection of the claim that most people believe that the Loch Ness monster exists.

C.

Fail to rejectFail to reject

Upper H 0H0.

There

is notis not

sufficient evidence to warrant rejection of the claim that most people believe that the Loch Ness monster exists.

D.

RejectReject

Upper H 0H0.

There

is notis not

sufficient evidence to warrant rejection of 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.

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

B.

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

C.

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

D.

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

Click to select your answer(s).

Answer 1

Appropriate hypotheses would be -

H0 : p = 0.50

Ha : p > 0.50

Observed value of test statistic =

where \hat{p} = 0.61 and n = 21019

then after putting the values above we get,

test statistic = 35.484

At 5% level of significance we have P-value = P(Z > 35.484)

= 0

as P-value is less than level of significance (0.05) then we can say that null hypothesis is rejected at 5% level of significance.

And hence we have sufficient evidence to claim that most people beleive that Loch ness monster exists.

Since sample size is large, conclusion is valid.