๐ Topic Summary
A confidence interval provides a range of values, calculated from sample data, that is likely to contain the true value of a population parameter (like the mean). It quantifies the uncertainty associated with estimating population parameters from a sample. The level of confidence (e.g., 95%) indicates the percentage of times that the interval would contain the true parameter if we were to repeat the sampling process many times.
Confidence intervals are influenced by sample size, variability in the sample (standard deviation), and the desired level of confidence. A larger sample size generally leads to a narrower confidence interval, while a higher level of confidence leads to a wider interval. Understanding these factors is crucial for correctly interpreting and applying confidence intervals in various statistical analyses.
๐ง Part A: Vocabulary
Match the following terms with their correct definitions:
- Confidence Level
- Margin of Error
- Population Parameter
- Sample Statistic
- Standard Error
Definitions:
- The extent to which the sample statistic may differ from the population parameter.
- A numerical value that characterizes some aspect of a population.
- A measure of the variability of a statistic from sample to sample.
- The probability that the confidence interval contains the true population parameter.
- A numerical value that summarizes data from a sample.
Match the term number to the definition number.
๐ Part B: Fill in the Blanks
Complete the following paragraph with the correct terms:
A __________ interval estimates a population __________ based on a sample __________. The width of the interval is affected by the __________ size and the desired __________ level. A larger sample size generally leads to a __________ interval.
๐งช Part C: Critical Thinking
Explain in your own words how increasing the sample size affects the width of a confidence interval and why this happens.