Question

As a condition of employment, Fashion Industries applicants must pass a drug test. Of the last 220 applicants, 14 failed the test. Develop a 99% confidence interval for the proportion of applicants that fail the test. Would it be reasonable to conclude that more than 10% of the applicants are now failing the test?

Answer 1

Of the last 220 applicants, 14 failed the test.

So, we have the sample proportion =
`(14)/(220)` = 0.064

At 99% confidence interval, z score is 2.576

Standard error or E =
`0.064+2.576* ((√(0.064*(1-0.064)) )/(√(220) ) )` and
`0.064-2.576* ((√(0.064*(1-0.064)) )/(√(220) ) )`

=
`0.064+0.04250` and
`0.064-0.04250`

= 0.0215, 0.1065

Rounding off we get 0.02,0.11

In percentage the applicants who failed lies between interval 2% and 11%.

So, yes it would be reasonable to conclude that more than 10% of the applicants are now failing the test.