Question

A quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective.

Step 1 of 2:

Suppose a sample of 865 floppy disks is drawn. Of these disks, 805 were not defective. Using the data, estimate the proportion of disks which are defective. Enter your answer as a fraction or a decimal number rounded to three decimal places.

Step 2 of 2:

Suppose a sample of 865 floppy disks is drawn. Of these disks, 805 were not 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,

n = 865

805 are not defective

x = 865 - 805 = 60 defective

Step 1)

Point estimate = sample proportion = = x / n = 60 / 865 = 0.069

1 - = 1 - 0.69 = 0.931

Step 2)

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= 1.96 * (((0.069* 0.931) /865 )

= 0.017

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.069 - 0.017 < p < 0.069 + 0.017

0.052 < p < 0.086

The 95% confidence interval for the population proportion p is : (0.052 , 0.086)