Question

Suppose a sample of 1996 floppy disks is drawn. Of these disks, 319 were defective. Using the data, construct the 99% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places

Answer 1

To construct a 99% confidence interval for the population proportion of defective floppy disks, calculate the sample proportion, standard error, find the critical value, and substitute values into the formula.

Step-by-step explanation:

To construct a 99% confidence interval for the population proportion of defective floppy disks, we can use the formula:

p ± Z · √((p(1-p))/n)

1. First, calculate the sample proportion (p) by dividing the number of defective disks (319) by the total number of sampled disks (1996) - p = 319/1996 = 0.16.
2. Next, calculate the standard error (SE) by using the formula: SE = √((p(1-p))/n) = √((0.16(1-0.16))/1996) = 0.009.
3. Then, find the critical value (Z) for a 99% confidence interval. Since the sample size is large, we can use the standard normal distribution. The critical value for a 99% confidence interval is approximately 2.576.
4. Finally, substitute the values into the formula to calculate the confidence interval: 0.16 ± 2.576 · 0.009 = (0.142, 0.178).