Answer:
The 98% confidence interval for the proportion of applicants that fail the test is (0.025, 0.067).
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 .
For this problem, we have that:
560 random tests conducted, 26 employees failed the test. This means that
98% confidence level
So , z is the value of Z that has a pvalue of
, so
.
The lower limit of this interval is:
The upper limit of this interval is:
The 98% confidence interval for the proportion of applicants that fail the test is (0.025, 0.067).