Trials in an experiment with a polygraph include 96 results that include 23 cases of wrong results and 73 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.
Find what the Test statistic z=
Find the p-value=
Solution :
This is the left tailed test .
The null and alternative hypothesis is
H0 : p = 0.80
Ha : p < 0.80
n = 96 = ( 73 cases correct +23 cases is wrong )
x = 73
= x / n = 73 / 96 =0.76
P0 = 0.80
1 - P0 = 1 - 0.80 =0.20
Test statistic = z
= - P0 / [P0 * (1 - P0 ) / n]
= 0.76 -0.80/ [(0.80*0.20) / 96 ]
= -0.97
Test statistic = z = -0.97
P(z < -0.97) = 0.1660
P-value = 0.1660
= 0.01
P-value >
0.1660 > 0.01
Fail to reject the null hypothesis .
There is not sufficient evidence to conclude that the porporation P0 is less than 80%
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