Answer:
A sample of 767 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
The margin of error is given by:
For this problem, we have that:
14 defectives out of 160, so
95% confidence level
So , z is the value of Z that has a pvalue of , so .
How many units would have to be sampled to be 95% confident that you can estimate the fraction of defective parts within 2% of the percentage?
We would need a sample of n.
n is fround when . So
Rounding up
A sample of 767 is needed.