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 10871087 floppy disks is drawn. Of these disks, 108 were defective. Using the data, construct the 95% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 108 / 1087 = 0.099

Z_/2 = 1.96

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

= 1.96 * (((0.099 * 0.901) / 1087)

= 0.017

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.099 - 0.017 < p < 0.099 + 0.017

0.082 < p < 0.116

(0.082 , 0.116)