First, calculate the sample proportion of defective disks:
Sample proportion (p-hat) = 172/1434 = 0.1199
Next, calculate the standard error:
Standard error = sqrt((0.1199 * (1-0.1199)) / 1434) = 0.008
For a 98% confidence interval, we need to find the z-score for a 98% confidence level, which is 2.33.
Now, calculate the margin of error:
Margin of error = 2.33 * 0.008 = 0.01864
Finally, construct the confidence interval:
Lower bound = 0.1199 - 0.01864 = 0.10126
Upper bound = 0.1199 + 0.01864 = 0.13854
The 98% confidence interval for the population proportion of defective disks is (0.101, 0.139).
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 1434
floppy disks is drawn. Of these disks, 172
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.
1 answer