Overview
This lecture explains the difference between confidence intervals and hypothesis tests, both of which are tools for making statistical inferences about populations from samples.
Statistical Inference
- Statistical inference helps us understand large populations by analyzing smaller, manageable samples.
- The two main methods of statistical inference are confidence intervals and hypothesis tests.
- The purpose of both methods is to answer questions about the population using data from a sample.
Confidence Intervals
- Confidence intervals estimate a range of values within which a population parameter likely falls.
- This method is used when the goal is to approximate the actual value of a parameter (e.g., "What percent of Americans love kittens?").
- The answer is provided as a range (e.g., 60% to 70%) instead of a single number.
Hypothesis Testing
- Hypothesis tests are used to compare a sample statistic to a known value or status quo.
- The focus is on determining if a parameter equals, is greater than, or less than a particular value (e.g., "Is the percentage greater than 62%?").
- Hypothesis tests are appropriate when the question involves comparisons or inequalities (e.g., "more than 50%").
Example Applications
- Use a confidence interval to estimate the actual percentage of people who prefer Pepsi.
- Use a hypothesis test to determine if more than 50% of people prefer Pepsi, focusing on the comparison rather than the exact value.
Key Terms & Definitions
- Statistical Inference — Drawing conclusions about a population based on data from a sample.
- Confidence Interval — A range of values likely to contain the population parameter.
- Hypothesis Test — A procedure to compare sample data to a known or claimed population value.
Action Items / Next Steps
- Read and answer Example Five, parts A and B, identifying whether a confidence interval or hypothesis test is appropriate for each question.