rials in an experiment with a polygraph include 96 results that include 22 cases

Question

rials in an experiment with a polygraph include 96 results that include 22 cases of wrong results and 74 cases of correct results. 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. Let p be the population proportion of correct polygraph results. Identify the null and alternative hypotheses. Choose the correct answer below.

Explanation / Answer

Given that,
possibile chances (x)=74
sample size(n)=96
success rate ( p )= x/n = 0.7708
success probability,( po )=0.8
failure probability,( qo) = 0.2
null, Ho:p>0.8
alternate, H1: p<0.8
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.64
since our test is left-tailed
reject Ho, if zo < -1.64
we use test statistic z proportion = p-po/sqrt(poqo/n)
zo=0.77083-0.8/(sqrt(0.16)/96)
zo =-0.7144
| zo | =0.7144
critical value
the value of |z | at los 0.05% is 1.64
we got |zo| =0.714 & | z | =1.64
make decision
hence value of |zo | < | z | and here we do not reject Ho
p-value: left tail - Ha : ( p < -0.71443 ) = 0.23748
hence value of p0.05 < 0.23748,here we do not reject Ho
ANSWERS
---------------
null, Ho:p=0.8
alternate, H1: p<0.8
test statistic: -0.7144
critical value: -1.64
decision: do not reject Ho
p-value: 0.23748

Related Questions

Navigate

• Browse (All)
• Browse R
• Subjects

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