Question

Trials in an experiment with a polygraph include 98 results that include 22 cases of wrong results and 76 cases of correct results. Use a 0.05 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.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.80

H_a : p < 0.80

= x / n = 76 / 98 = 0.7755

P₀ = 0.80

1 - P₀ = 0.20

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.7755 - 0.80 / [(0.80 * 0.20) / 98]

= -0.606

P(z < -0.606) = 0.2723

P-value = 0.2723

= 0.05

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to test the claim that such polygraph results are correct less than 80​% of the time .