Confidence intervals for the difference between two proportions | AP Statistics | Khan Academy

TL;DR

Learn how to construct confidence intervals for proportions by setting up conditions for inference, calculating critical values, and using sample proportions to estimate the standard deviation.

Transcript

• [Instructor] Let's review calculating confidence intervals for proportions. So let's say I have a population, and I care about some proportion. Let's say I care about the proportion of folks that are left-handed. I don't know what that is, and so I take a sample of size n, and then from that sample, I can calculate a sample proportion. That's why... Read More

Key Insights

• ⚾ Confidence intervals for proportions are used to estimate the true population proportion based on a sample.
• 👷 Conditions for inference, such as random sampling, normal distribution, and independence, must be met before constructing confidence intervals.
• ⌛ The confidence level determines the percentage of times the confidence interval would overlap with the true population proportion.

Questions & Answers

Q: What are the conditions for constructing confidence intervals for proportions?

The conditions include random sampling, a normal sampling distribution (n times the sample proportion and n times one minus the sample proportion should be greater than or equal to 10), and independence (either done with replacement or the sample size is no more than 10% of the population size).

Q: How is a confidence level determined for a confidence interval?

A confidence level, such as 95%, is chosen to indicate the percentage of times the confidence interval would overlap with the true population proportion. A critical value is calculated based on this confidence level.

Q: How is the standard deviation of the sampling distribution estimated?

The standard deviation, or standard error, is estimated using the sample proportion to calculate the square root of p hat times one minus p hat over n. This is done because the true population parameter is unknown.

Q: How is a confidence interval constructed for the difference between two proportions?

Similar to constructing a confidence interval for one proportion, conditions for inference must be met. Then, the critical value and standard deviation (which is the sum of the variances of each sample proportion) are used to calculate the confidence interval.

Summary & Key Takeaways

• Confidence intervals are used to estimate the true proportion of a population by taking a sample and calculating a sample proportion.

• Conditions for inference must be met, including random sampling, normal sampling distribution, and independence.

• A confidence level is set, and a critical value and standard deviation of the sampling distribution are calculated to construct the confidence interval.