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. estimate of defective disks =.140

Answer 1

Solution :

Given that,

n = 815

x = 114

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

1 - = 1 - 140 = 0.860

At 90% confidence level

= 1 - 90%

=1 - 0.90 = 0.10

/2 = 0.05

Z/2 = Z_{0.05 = 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

0.140  ± 0.020

(0.120 , 0.160)