Overview
This lecture covers how to determine the minimum sample size needed for research when working with proportions, emphasizing the relationship between confidence level, margin of error, and sample size.
Importance of Sample Size
- Sample size is crucial in research and directly affects confidence and error.
- Determining "how big is big enough" depends on desired confidence and margin of error.
Sample Size Formula for Proportions
- Researchers predetermine the desired confidence level and margin of error before data collection.
- A specific formula calculates the minimum sample size for proportions, given a confidence level and margin of error.
- The formula uses the z* value (critical value) corresponding to the confidence level.
- The margin of error must be converted from percent to decimal when using the formula.*
Application Example
- For 95% confidence and 3% margin of error: use z* = 1.96 and error = 0.03.
- Calculated sample size may be a decimal; always round up to the next whole number when sampling people.
- In the example, a sample size of 1,167.11 rounds up to 1,168 voters.*
Increasing Confidence and Decreasing Error
- A higher confidence level or a lower margin of error requires a larger sample size.
- Example: increasing confidence to 99% and lowering error to 2% raises the required sample size to 4,161.
- Achieving both higher confidence and lower error is only possible by increasing sample size.
Research and Exam Relevance
- Determining sample size is the first step in planning any research survey or experiment.
- Expect exam questions requiring use of the sample size formula for proportions.
Key Terms & Definitions
- Sample Size — Number of subjects needed in a study to achieve desired confidence and error.
- Confidence Level — Probability that the interval estimate contains the true population parameter.
- Margin of Error — Maximum expected difference between the true population value and a sample estimate.
- z* — Critical value from the standard normal distribution corresponding to a chosen confidence level.
- Proportion — Fraction or percentage of a population with a certain characteristic.
Action Items / Next Steps
- Practice calculating minimum sample sizes for various confidence levels and margins of error.
- Memorize the critical z* values for common confidence levels (e.g., 1.96 for 95%, 2.576 for 99%).
- Prepare for an exam question involving the sample size formula for proportions.*