Trials in an experiment with a polygraph include 98 results that include 23 case

Question

Trials in an experiment with a polygraph include 98 results that include 23 cases of wrong results and 75 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 nullhypothesis, and final conclusion that addresses the original claim. Use the P-value method. Use the normal distribution as an approximation of the binomial distribution.

A.) Test statistic z =

B.) P-value value =

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

Explanation / Answer

alpha,a = 0.05
p0 = 0.80
x = 75 , n = 98 , phat=x/n = 0.76
.
H0: p = 0.8
H1: p is not equal to 0.8
.
standard error, SE = sqrt(p0(1-p0)/n)
SE = sqrt(0.8(1-0.8) / 98) = 0.04039
.
test statistic, z = (phat-p0) / SE
z = (0.76-0.8) / 0.04039 = -0.99

Since it is a 2-tailed test, hence
P_value = 2*P(Z>|z|) = 2 * P(Z> 0.99 )
= 2*(1 - P(Z< 0.99 ))
= 2*(1 - 0.8389 )
= 0.3222

Since P_Value > 0.05(alpha), hence H0 can not be rejected
So we conclude that such results are correct 80% of the time.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.