Question

A quality-conscious disk manufacturer wishes to know the fraction of disks his company makes which are defective. Suppose a sample of 863 floppy disks is drawn, and of these disks, 717 were not defective. Using the data, construct the 90% confidence interval for the population proportion of disks that are defective. Round your answers to three decimal places.

Answer 1

To construct a 90% confidence interval, use the formula: Confidence interval = sample proportion ± (z-value × standard error). Calculate the sample proportion and standard error, find the z-value for a 90% confidence level, and substitute the values into the formula to calculate the confidence interval.

Step-by-step explanation:

To construct a 90% confidence interval for the population proportion of defective disks, we need to use the formula:

Confidence interval = sample proportion ± (z-value × standard error)

First, we calculate the sample proportion: 717/863 = 0.830.

The standard error of proportion can be calculated as: √((p(1-p))/n), where p is the sample proportion and n is the sample size.

Next, we find the z-value for a 90% confidence level, which is approximately 1.645.

Finally, we substitute the values into the formula to calculate the confidence interval. The lower limit is 0.806 and the upper limit is 0.854.