Ch 8 Estimating with Confidence 8.1: Confidence Intervals

Definitions Statistical Inference Statistical Inference –Provides methods for drawing conclusions about a population from sample data –What happens if I do this many times? Formal Inference Formal Inference –Using probability to express the strength of our conclusions (probability takes chance variation into account)

Margin of Error Margin of Error –How accurate we believe our guess is, based on the variability of the estimate –What you always see in the fine print

Confidence Intervals Use facts about sampling distributions (what would happen in the long run) to express our confidence in the results of any one sample Use facts about sampling distributions (what would happen in the long run) to express our confidence in the results of any one sample “We got these numbers by a method that gives correct results 95% of the time.” “We got these numbers by a method that gives correct results 95% of the time.” In the form of estimate ± margin of error In the form of estimate ± margin of error A confidence level, C, gives the overall success rate of the method for calculating the confidence interval. In C% of all possible samples, the method would yield an interval that captures the true parameter value. A confidence level, C, gives the overall success rate of the method for calculating the confidence interval. In C% of all possible samples, the method would yield an interval that captures the true parameter value.

Most Common Confidence Intervals 90% corresponds to the middle 90% of normal distribution z-score = (called the critical value) 95% corresponds to the middle 95% of normal distribution z-score = % corresponds to the middle 99% of normal distribution z-score = Interpretation: We are C% confident that the interval from _____ to ____captures the actual value of the population parameter in context.

Ways to Decrease Margin of Error Make z* smaller (decrease confidence level C) Make z* smaller (decrease confidence level C) Increase sample size n Increase sample size n Decrease standard deviation σ Decrease standard deviation σ –High Confidence – our method almost always gives correct answers –Small Margin of Error – we have pinned down the parameter quite precisely

Confidence Intervals Toolbox I Create Fabulous Confidence Intervals Identify Identify –Population –Parameter –Procedure Conditions Conditions Formula Formula Calculations Calculations Interpret in Context Interpret in Context