Question

Trials in an experiment with a polygraph include 97 results that include 22 cases of wrong results and 75 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: p = 0.80
H1: p > 0.80
B. H0: p = 0.20
H1: p ≠ 0.20
C. H0: p = 0.80
H1: p < 0.80
D. H0: p = 0.20
H1: p > 0.20
E. H0: p = 0.80
   H1: p ≠ 0.80
F. H0: p = 0.20
   H1: p < 0.20

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.
(1) -----------H0. There (2)------------ sufficient evidence to support the claim that the polygraph results are correct less than 80% of the time.

(1) Fail to reject
   Reject
(2) is not

Answer 1

C. H0: p = 0.80
H1: p < 0.80

The test statistic is z = -0.66

The P-value is 0.2546.

Fail to reject

is not