Question

A quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective. Step 2 of 2 : Suppose a sample of 425 floppy disks is drawn. Of these disks, 38 were defective. Using the data, construct the 85% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places.

Answer 1

Sample proportion = 38 / 425 = 0.089

From Z table,

Z/2 = 1.4395

Margin of error E = Z/2 * sqrt [ ( 1 - ) / n ]

= 1.4395 * sqrt [ 0.089 ( 1 - 0.089 ) / 425 ]

= 0.020

85% confidence interval for p is

- E < p < + E

0.089 - 0.020 < p < 0.089 - 0.020

0.069 < p < 0.109

85% CI is ( 0.069 , 0.109 )