Question

5.

Trials in an experiment with a polygraph include 96 results that include 22 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.

H0​:

p=0.20

H1​:

p≠0.20

B.

H0​:

p=0.80

H1​:

p≠0.80

C.

H0​:

p=0.20

H1​:

p<0.20

D.

H0​:

p=0.80

H1​:

p>0.80

E.

H0​:

p=0.20

H1​:

p>0.20

F.

H0​:

p=0.80

H1​:

p<

The test statistic is

z=

​(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.

▼

Reject

Fail to reject

H0.

There

▼

is not

is

sufficient evidence to support the claim that the polygraph results are correct less than

80​%

of the time.

Answer 1

H0: p = 0.80

Ha: p < 0.80

Sample proportion = 74 / 96 = 0.7708

Test statistics

z = ( - p) / sqrt [ p (1 - p ) / n ]

= ( 0.7708 - 0.80) / sqrt [ 0.80 ( 1 - 0.80) / 96 ]

= -0.72

p-value = P(Z < z)

= P(Z < -0.72)

= 0.2358

Since p-value > 0.01 level, fail to reject H0

There is not sufficient evidence to support the claim that the polygraph results are correct less than

80% of the time.