Question

HighTech, Inc. randomly tests its employees about company policies. Last year in the 550 random tests conducted, 24 employees failed the test.

1. Develop a 95% confidence interval for the proportion of applicants that fail the test. (Round your answers to 3 decimal places.)

2. Would it be reasonable to conclude that 6% of the employees cannot pass the company policy test?

• No

• Yes

Answer 1

a)

Sample proportion = 24 / 550 = 0.044

95% confidence interval for p is

- Z/2 * sqrt [ ( 1 - ) / n ] < p < + Z/2 * sqrt [ ( 1 - ) / n ]

0.044 - 1.96 * sqrt [ 0.044 * ( 1 - 0.044) / 550] < p < 0.044 + 1.96 * sqrt [ 0.044 * ( 1 - 0.044) / 550]

0.027 < p < 0.061

95% CI is ( 0.027 , 0.061 )

b)

Since 6% ( or 0.06) contained in confidence interval, Yes we have enough evidence to say that 6% of the

employees can not pass the company policy test.