Sample Size and Confidence Intervals

This lesson demonstrates how to use Desmos to calculate the sample size needed for a proportion confidence interval. It covers determining the margin of error, finding the Z-score for a 95% confidence level, and making assumptions about sample proportions. The video provides step-by-step instructions on using Desmos to perform these calculations, including entering formulas and adjusting sliders. The final sample size is calculated to ensure a 3% margin of error at a 95% confidence level.

What is the main purpose of using Desmos in this lesson?

• To calculate the mean and standard deviation

• To perform hypothesis testing

• To determine the sample size needed for a confidence interval

• To create graphs for data visualization

What is the margin of error specified by the political candidate?

• 2%

• 4%

• 5%

• 3%

What is the z-score for a 95% confidence level?

• 2.58

• 2.33

• 1.96

• 1.64

What assumption is made about the sample proportion when no information is given?

• 40% support, 60% don't support

• 60% support, 40% don't support

• 70% support, 30% don't support

• 50% support, 50% don't support

Which function in Desmos is used to find the z-score?

• Standard Deviation

• Inverse CDF

• Mean Calculation

• Normal Distribution

What is the formula used to calculate the sample size 'n'?

• n = (z * (1-p)) / e^2

• n = (z^2 * p^2) / e

• n = (z^2 * p * (1-p)) / e^2

• n = (z * p) / e

What value is used for 'p' in the sample size formula when no prior information is available?

• 0.9

• 0.7

• 0.5

• 0.3

Why is it important to round up the sample size calculation?

• To increase the confidence level

• To reduce the margin of error

• To make calculations easier

• To ensure the sample size is not too small

What is the final sample size needed for the given margin of error and confidence level?

• 1050

• 1070

• 1068

• 1067

What is the confidence level used in this lesson?

• 85%

• 95%

• 99%

• 90%