Answer:
If, p-value<α reject the null hypothesis, hence the production process is not really out of control.
Step-by-step explanation:
From the information, observe that a manufacturer considers his production process to be out of control when defects exceeds 3%. Consider a random sample of 85 items, the defect rate is 5.9%.
Here, The claim is that this is the only sample fluctuation and production is not really out of control.
Consider a null and alternative hypothesis:
Null hypothesis, H_o: The production process is not out of control when the defect does not exceed 3%.
that is H_o: p<=0.03
Alternative hypothesis, H_a: the production process to be out of control when defect exceeds 3%
That is H_a: p>0.03:
Level of significance α= 0.01
Test statistics under null hypothesis. [tex]z= \frac{p-p}{\sqrt{\frac{pq}{n} } }[/tex]
[tex]z= \frac{0.059-0.03}{\sqrt{\frac{0.03(1-0.03)}{85} } }[/tex]
=[tex]\frac{0.029}{0.0185}[/tex]
= 1.57
Calculative p-values as follows
P(z>1.57)= 1-P(z<=1.57)
= 1-0.9418
=0.0582
compare the p value with level significance
If, p-value<α reject the null hypothesis, hence the production process is not really out of control.
