Question

Trials in an experiment with a polygraph include 97 97 results that include 23 23 cases of wrong results and 74 74 cases of correct results. Use a 0.01 0.01 significance level to test the claim that such polygraph results are correct less than 80 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.

Answer 1

Hypotheses:

Null hypothesis: p = 0.80

Alternative hypothesis: p < 0.80 [Left - Tailed Test]

Sample proportion = 74/97 = 0.763

Hence,

Test statistic

z = -0.91

p - Value = P(z < -0.91) = 0.1804

Since p - value is greater than 0.01 significance level, we do not reject Ho and hence, we do not have sufficient reason to conclude that such polygraph results are correct less than 80​% of the time.