Trials in an experiment with a polygraph include 98 results that include 24 cases of wrong results and 74 cases of correct resul
ts. 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.
<span>Answer:
Let P be the proportion of correct results of all polygraph results
H0: P ≥ 0.80
Ha: P < 0.80
Estimated p = 74 / 98 = 0.7551
Variance of proportion = p*(1-p)/n
= 0.8(0.2)/98 =0.0016327
S.D. of p is sqrt[0.001633] = 0.0404
z = ( 0.7551 - 0.8 ) / 0.0404 = -1.1112
P-value = P( z < -1.1112) = 0.1335
Since the p-value is greater than 0.05, we do not reject the null hypothesis. Based on the results there is no evidence that polygraph test results should be prohibited as evidence in trials.</span>
Side-Angle-Side is a rule used to prove whether a given set of triangles are congruent. The SAS rule states that: If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent.
