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 464 floppy disks is drawn. Of these disks, 51 were defective. Using the data, construct the 80% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places.

Answer 1

Standard error of the mean = SEM = √x(N-x)/N³ = 0.015

α = (1-CL)/2 = 0.100

Standard normal deviate for α = Z_α = 1.282

Proportion of positive results = P = x/N = 0.110

Lower bound = P - (Z_α*SEM) = 0.091

Upper bound = P + (Z_α*SEM) = 0.129