Question

Trials in an experiment with a polygraph include 9898 results that include 2222 cases of wrong results and 7676 cases of correct results. Use a 0.010.01 significance level to test the claim that such polygraph results are correct less than 8080​% 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.

b) The test statistic is z=

c) The​ P-value is=

Answer 1

The statistical software output for this problem is:

One sample proportion summary hypothesis test:

p : Proportion of successes
H0 : p = 0.8
HA : p < 0.8

Hypothesis test results:

Proportion	Count	Total	Sample Prop.	Std. Err.	Z-Stat	P-value
p	76	98	0.7755102	0.040406102	-0.60609153	0.2722

Hence,

b) Test statistic = -0.61

c) P value = 0.272