Questions: Question 6 of 8, Step 2 of 2 8 / 12 Correct 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 865 floppy disks is drawn. Of these disks, 69 were defective. Using the data, construct the 95% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places. Lower endpoint: Upper endpoint:

Question 6 of 8, Step 2 of 2 8 / 12 Correct 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 865 floppy disks is drawn. Of these disks, 69 were defective. Using the data, construct the 95% confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places. Lower endpoint: Upper endpoint:
Transcript text: Question 6 of 8, Step 2 of 2 $8 / 12$ Correct 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 865 floppy disks is drawn. Of these disks, 69 were defective. Using the data, construct the $95 \%$ confidence interval for the population proportion of disks which are defective. Round your answers to three decimal places. Answer Tables How to enter your answer (opens in new window) Keyboard S Previous step Lower endpoint: $\square$ Upper endpoint: $\square$
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Solution

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Solution Steps

Step 1: Calculate the sample proportion of defective items

Given a sample size of 865 and 69 defective items, the sample proportion \(p\) is calculated as \(p = \frac{69}{865} = 0.0798\).

Step 2: Calculate \(q = 1 - p\)

\(q = 1 - 0.0798 = 0.92\).

Step 3: Determine the Z-score

For a confidence level of 95%, the Z-score is approximately 1.96.

Step 4: Calculate the standard error of the proportion

The standard error \(SE\) is calculated as \(SE = \sqrt{\frac{p \cdot q}{n}} = 0.0092\).

Step 5: Calculate the margin of error

The margin of error \(ME\) is \(ME = Z \cdot SE = 0.0181\).

Step 6: Determine the confidence interval

The confidence interval is from 0.062 to 0.098.

Final Answer:

The 95% confidence interval for the population proportion of defective items is from 0.062 to 0.098, rounded to 3 decimal places.

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