Answer:
H0:p= 0.80 H1: p< 0.80 one tailed test
Step-by-step explanation:
We state the null and alternative hypotheses as that the results are 80 % against the claim that the results are less than 80%.
H0:p= 0.80 H1: p< 0.80 one tailed test
p2= 0.8 , p1= 74/97= 0.763
q1= 1-0.763= 0.237 q2= 0.2
The level of significance is 0.05 .
The Z∝= ±1.645 for ∝= 0.05
The test statistic used here is
Z= p1-p2/ √pq/n
Putting the values:
Z= 0.763 -0.8 / √ 0.8*0.2/97
z= -0.037/ 0.0406
z= -0.9113
The Z∝ = ±1.645 for ∝= 0.05 for one tailed test.
As the calculated value does not fall in the critical region we fail to reject the null hypothesis. There is not sufficient evidence to support the claim that such polygraph results are correct less than 80% of the time.
Using the normal probability table.
P (Z < -0.9113)= 1- P(z= 0.9311) = 1- 0.8238= 0.1762
If P- value is smaller than the significance level reject H0.
0.1762> 0.005 Fail to reject H0.
