Question

As a condition of employment, Fashion Industries applicants must pass a drug test. Of the last 210 applicants, 24 failed the test.

(1) Develop a 90% confidence interval for the proportion of applicants that fail the test. (Round your answers to 3 decimal places.)

(2) Yes or no...Would it be reasonable to conclude that more than 7% of the applicants are now failing the test?

Answer 1

Solution :

Given that,

n = 210

x = 24

= x / n =24 /210 = 0.114

1 - = 1 - 0.114 = 0.886

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 * (((0.114 * 0.886) / 210) = 0.036

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.114 - 0.036 < p < 0.114 + 0.036

0.078 < p < 0.150

The 90% confidence interval for the population proportion p is : ( 0.078 , 0.150)

(2) yes