Determining sample size based on confidence and margin of error | AP Statistics | Khan Academy

TL;DR

Della wants to estimate the proportion of her community in favor of a tax increase for local school funding. She needs a minimum sample size of 2,401 to achieve a margin of error of no more than 2% at a 95% confidence level.

Transcript

• [Instructor] We're told Della wants to make a one-sample z interval to estimate what proportion of her community members favor a tax increase for more local school funding. She wants her margin of error to be no more than plus or minus 2% at the 95% confidence level. What is the smallest sample size required to obtain the desired margin of error?... Read More

Key Insights

• 🪡 Della needs a minimum sample size of 2,401 to achieve a margin of error of no more than 2% at a 95% confidence level.
• ❓ The margin of error is calculated using the formula: critical value * standard error of the statistic.
• ❓ The standard error of the sample proportion is determined by the sample proportion, (1 - sample proportion), and the sample size.
• ❓ The maximum sample proportion (0.5) is assumed to maximize the margin of error calculation.

Questions & Answers

Q: What does Della want to estimate about her community members?

Della wants to estimate the proportion of community members who favor a tax increase for local school funding.

Q: What is the margin of error?

The margin of error is the range within which the true population proportion is estimated to lie. Della wants the margin of error to be no more than 2%.

Q: How is the sample proportion calculated?

The sample proportion is calculated by taking a random sample and dividing the number of individuals in favor of the tax increase by the total sample size.

Q: What is the critical value for a 95% confidence level?

The critical value for a 95% confidence level is 1.96. This value is used to determine the range of the confidence interval.

Summary & Key Takeaways

• Della wants to estimate the proportion of her community members in favor of a tax increase for local school funding.

• She aims to have a margin of error of no more than 2% at a confidence level of 95%.

• To determine the minimum sample size needed, she uses the formula for constructing a confidence interval and solves for n.