Question

Trials in an experiment with a polygraph include 97 results that include 23 cases of wrong results and 74 cases of correct results. Use a 0.01 significance level to test the claim that such polygraph results are correct less than 80​% of the time. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method. Use the normal distribution as an approximation of the binomial distribution.

Let p be the population proportion of correct polygraph results. Identify the null and alternative hypotheses. Choose the correct answer below.

A. H0​: pequals0.20 H1​: pnot equals0.20

B. H0​: pequals0.20 H1​: pless than0.20

C. H0​: pequals0.20 H1​: pgreater than0.20

D. H0​: pequals0.80 H1​: pgreater than0.80

E. H0​: pequals0.80 H1​: pless than0.80

F. H0​: pequals0.80 H1​: pnot equals0.80

The test statistic is zequals _______. ​(Round to two decimal places as​ needed.)

The​ P-value is -------. ​(Round to four decimal places as​ needed.)

Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim.

▼ RejectOR Fail to reject H0. There ▼ isOR not is sufficient evidence to support the claim that the polygraph results are correct less than 80​% of the time.

Answer 1

n=97, x=74, P= 80%= 0.80, = 0.01

a)

Ho: p = 0.80

H1: p <  0.80

b)

z = -0.91

Test statistics = -0.91

c)

P-Value = P(z < -0.91)

using normal z table we get

P(z < -0.91) = 0.1804

P-Value = 0.1804

d)

since (P-Value = 0.1804 ) > ( = 0.01)

Failed to reject the null hypothesis.

Fail to reject H0. There is not isufficient evidence to support the claim that the polygraph results are correct less than 80​% of the time.