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+ The Practice of Statistics, 4 th edition – For AP* STARNES, YATES, MOORE Chapter 8: Estimating with Confidence Section 8.1 Confidence Intervals: The Basics Section 8.2 Estimating a Population Proportion

+ 2 Chapter 8 Estimating with Confidence 8.1Confidence Intervals: The Basics 8.2Estimating a Population Proportion 8.3Estimating a Population Mean

+ 3 Interpreting Confidence Levels and Confidence Intervals The confidence level is the overall capture rate if the method is used many times. Confidence level: To say that we are 95% confident is shorthand for “95% of all possible samples of a given size from this population will result in an interval that captures the unknown parameter.” Confidence interval: To interpret a C% confidence interval for an unknown parameter, say, “We are C% confident that the interval from _____ to _____ captures the actual value of the [population parameter in context].” Interpreting Confidence Level and Confidence Intervals Confidence Intervals: The Basics

+ 4 Constructing a Confidence Interval estimate ± margin of error A more general formula for confidence intervals: statistic ± (critical value) (standard deviation of statistic) Confidence Intervals: The Basics The margin of error gets smaller when: The confidence level decreases The sample size n increases

+ 5 Using Confidence Intervals Before calculating a confidence interval for µ or p there are three important conditions that you should check. 1) Random: The data should come from a well-designed random sample or randomized experiment. 2) Normal: The sampling distribution of the statistic is approximately Normal. 3) Independent: Individual observations are independent. Confidence Intervals: The Basics NOTE: --these methods assume SRS (not stratified or cluster sampling) --margin of error describes error from chance variation in randomization, NOT error from undercoverage and nonresponse.

+ 6 Chapter 8 Estimating with Confidence 8.1Confidence Intervals: The Basics 8.2Estimating a Population Proportion 8.3Estimating a Population Mean

+ 7 Activity: The Beads Your teacher has a container of different types of beans. Your goal is to estimate the actual proportion of brown beans in the container. Form teams of 3 or 4 students. Determine how to use a cup to get a simple random sample of beans from the container. Each team is to collect one SRS of beans. Determine a point estimate for the unknown population proportion. Find a 90% confidence interval for the parameter p. Consider any conditions that are required for the methods you use. Compare your results with the other teams in the class. Estimating a Population Proportion

+ 8 Conditions for Estimating p Random: The sample must be an SRS taken from the population. Normal: Both np and n(1 – p) must be greater than 10. Independent: If the sample is done without replacement, we must check the 10% condition. Estimating a Population Proportion p482 #13, 17, 19-26 p496 #27,29 If all three conditions are met, it is safe to construct a confidence interval.

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