Question

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 .05 significance level to test the claim that such polygraph results are correct less than80%of the time. Identify the null hypothesis, alternative hypothesis, test statistic, the conclusion about the null hypothesis, and the final conclusion that addresses the original claim.

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

The test statistic is z =

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

Reject/ fail to reject H0. There is/is not sufficient evidence to support the claim that the polygraph results are correct less than 80 %of the time.

Answer 1

Given that, sample size ( n ) = 96

significance level = 0.05

Point estimate for correct result = 74/96 = 0.7708

The null and alternative hypotheses are,

H₀ : p = 0.80

H_a : p < 0.80

Test statistic is,

Test statistic is, z = -0.72

P-value = P(Z < -0.72) = 0.2358

Here, p-value = 0.2358 >

Implies that we fail to reject the null hypothesis ( H₀)

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