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Confidence Interval for a Proportion

Author:Matt Forbes, Steve Phelps
The applet below illustrates the concept of constructing confidence intervals for proportions (a 1-proportion z-interval). Set the population proportion, sample size, and confidence level using the sliders. There are 100 confidence intervals at your chosen confidence level, based on 100 random samples of your chosen sample size, from a population with your chosen proportion. On average, the percentage of confidence intervals that contain the population proportion will be equal to the chosen confidence level. The following applet is for you to play and explore. Once you have experimented with different proportions, sample sizes, and confidence levels, proceed to the questions below.

1. If we change the population proportion to 0.6, the sample size to 40, and the confidence level to 0.85, what % of the confidence intervals will capture the population proportion? Choose your answer before using the applet to find it.

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2. What happens to the width of the confidence interval when we increase the sample size?

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3. What happens to the width of the confidence interval when we increase the confidence level?

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4. You hopefully noticed that larger sample sizes produced shorter confidence intervals. Explain why you think this would be true.

5. You hopefully noticed that larger confidence levels produced longer confidence intervals. Explain why this would be true.

To interpret a confidence level of 0.95 we could say the following: If we were to select many random samples from a population and construct a 95% confidence interval using each sample, about 95% of the intervals would capture the true population proportion.

6. Interpret a confidence level of 0.75.

A confidence interval consists of two parts. A point estimate is at the center of our interval and is a statistic that provides an estimate of a population parameter. The margin of error is the distance from the point estimate to the edge of our confidence interval. Thus, the difference between the point estimate and the true parameter value will be less than the margin of error in C% of all samples, where C is the confidence level.

7. If we have a confidence interval (0.42, 0.64), what is the point estimate?

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8. If we have a confidence interval (0.42, 0.64), what is the margin of error?

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