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 815 floppy disks is drawn. Of these disks, 114 were defective. Using the data, construct the 90% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places.

Answer 1

Solution :

Given that,

n = 815

x = 114

Point estimate = sample proportion = = x / n = 114/815 = 0.140

1 - = 1- 0.140 = 0.860

Z_/2 = '1.645

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

= 1.645 * ((0.140*(0.860) /815 )

= 0.020

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.140- 0.020 < p < 0.140+ 0.020

0.120< p < 0.160

The 90% confidence interval for the population proportion p is : 0.120,0.160