To construct a 99.9% confidence interval for the proportion of people who performed volunteer work, we can use the formula for the confidence interval for a proportion:
Where:
- is the sample proportion
- is the sample size
- is the z-value corresponding to the desired confidence level (for a 99.9% confidence level, )
From the previous calculation, we found:
Step 1: Calculate the standard error (SE)
Calculating this step-by-step:
-
Calculate :
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Divide by :
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Take the square root:
Step 2: Calculate the margin of error (ME)
Now we compute the margin of error using the z-value for 99.9% confidence:
Step 3: Calculate the confidence interval
Now we can construct the confidence interval:
So the interval is:
Calculating this gives:
Step 4: Round the results
Rounding each end of the interval to at least three decimal places, we obtain:
Final Result
Thus, a 99.9% confidence interval for the proportion of people who performed volunteer work during the past year is: