The Practice of Statistics Third Edition Yates, Moore & Starnes Chapter 10: Estimating with Confidence

Chapter Objectives Describe statistical inference Describe the basic form of all confidence intervals Construct and interpret a confidence interval for a population mean (including paired data) and for a population proportion Describe a margin of error, and explain ways in which you can control the size of the margin of error Determine the sample size necessary to construct confidence interval for a fixed margin of error Compare and contrast the t distribution and the Normal distribution List the conditions that must be present to construct a confidence interval for a population mean or a population proportion Explain what is meant by the standard error, and determine the standard error of x-bar and the standard error of p-hat.

Introduction Objectives Explain what is meant by statistical inference Explain how probability is used to make conclusions about statistical inference

Readability Activity We want to infer from the sample data some conclusion about the population Excel function to select 14 pages =RANDBETWEEN(13,341) 31, 34, 45, 48, 70, 132, 133, 181, 183, 257, 281, 282, 284, 306, 307

Confidence intervals Significance tests When you use statistical inference, you are acting as if the data are a random sample or come from a randomized experiment !

Today’s 10.1 Objectives There are more objectives for this section, but here are today’s: List the (six) basic steps in the reasoning of statistical estimation Distinguish between a point estimate and an interval estimate Identify the basic form of all confidence intervals Explain what is meant by margin of error

Inference is the process of trying to say something about a population from information we can get from a sample. Sample values (____________) vary but the population values (_____________) do not. Any given sample value may or may not be helpful in understanding a population value. Only by considering our sample as one of many such samples can we draw inferences. (Examples illustrate this process.)

Six Steps of Estimation from page 619

Confidence Interval Applet of publisher’s website may be helpful in clarifying steps 4 & 5.

One of the most common mistakes students make on the AP Exam is misinterpreting the information given by a confidence interval. There seems to be an almost irresistible urge to attach meaning in terms of probability to a found interval. Probabilities are long-run relative frequencies, and the idea simply doesn’t apply to a found interval. An already constructed interval either does or does not contain the population value. While it is correct to give the meaning of “confidence” in terms of probability (that is, “the probability that my method of constructing intervals will capture the true population value is 0.95”), it is never correct to interpret a found interval using the language of probability.

IMPORTANT: In a confidence interval, our “confidence” is in the procedure used to generate the interval. That is, we are “confident” that an interval so constructed will contain the true population value 95% (or whatever the appropriate confidence level) of the time.

Confidence Interval Applet (p 623-4) Activity 10B

Practice: P