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 4447 floppy disks is drawn. Of these disks, 311 were 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 4447 floppy disks is drawn. Of these disks, 311 were defective. Using the data, construct the 98% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places.

Lower Endpoint:

Upper Endpoint:

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 0.070

Z_/2 = 2.326

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

= 2.326 * (((0.070 * 0.930) / 4447)

= 0.009

A 98% confidence interval for population proportion p is ,

- E < p < + E

0.070 - 0.009 < p < 0.070 + 0.009

0.061 < p < 0.079

Lower endpoint = 0.061

Upper endpoint = 0.079