Introduction
When estimating a population proportion, it is essential to calculate the width of the confidence interval to determine the range within which the true population proportion lies. In this article, we will explore how to determine the width of a confidence interval based on a sample proportion and margin of error.
Calculating the Width of the Confidence Interval
To calculate the width of a confidence interval, we need to consider the sample proportion, margin of error, and confidence level. In this case, we have a sample proportion of 18 percent and a margin of error of 4 percent, with a 90 percent confidence interval.
First, we calculate the standard error using the formula:
Standard Error = √(p*(1-p)/n)
where p is the sample proportion and n is the sample size. Using p = 0.18 (18 percent) and n = sample size, we can determine the standard error.
Next, we calculate the margin of error by multiplying the standard error by the critical value corresponding to the desired confidence level. For a 90 percent confidence level, the critical value is approximately 1.645.
Margin of Error = Critical Value * Standard Error
Finally, we calculate the width of the confidence interval by adding and subtracting the margin of error from the sample proportion:
Width of Confidence Interval = Sample Proportion ± Margin of Error
Example Calculation
Suppose we have a sample proportion of 18 percent and a margin of error of 4 percent. Using the formulas mentioned above, we can calculate the width of the confidence interval as follows:
- Standard Error = √(0.18*(1-0.18)/n)
- Margin of Error = 1.645 * Standard Error
- Width of Confidence Interval = 18% ± Margin of Error
Conclusion
Calculating the width of a confidence interval is crucial in estimating the true population proportion within a specified range. By understanding the formulas and steps involved, researchers and analysts can confidently interpret the results of their studies and make informed decisions based on these estimates.
