Chapters 19,23 Confidence Intervals.ppt

From the Data at Hand to the World at LargeChapters 19, 23Confidence Intervals Estimation of population parameters: an unknown population proportion p an unknown population mean ? Concepts of Estimation The objective of estimation is to estimate the unknown value of a population parameter, like the mean ?, on the basis of a sample statistic calculated from sample data. ? e.g., NCSU housing office may want to estimate the mean distance ? from campus to hometown of all students There are two types of estimates Point Estimate Interval estimate What do we frequently need to estimate? An unknown population proportion p An unknown population mean ? ?? p? Point Estimates The sample mean is the best point estimate of the population mean ? p = , the sample proportion of x successes in a sample of size n, is the best point estimate of the population proportion p ^ Example: Estimating an unknown population proportion p Is Herb Sendeks departure good or bad for States mens basketball team? (Technician opinion poll; not scientifically valid!!) In a sample of 1000 students, 590 say that Sendek’s departure is good for the bb team. p = 590/1000 = .59 is the point estimate of the unknown population proportion p that think Sendek’s departure is good. ^ Example: Estimating an unknown mean ? In an effort to improve drive-through service, a Burger King records the drive-through service times of 52 randomly selected vehicles. The sample mean service time =181.3 seconds is the point estimate of the unknown mean service time ? Shortcoming of Point Estimates = 181.3 seconds, best estimate of mean service time ? p = 590/1000 = .59, best estimate of population proportion p BUT How good are these best estimates? No measure of reliability A confidence interval is a range (or an interval) of values used to estimate the unknown value of a population parameter . /US/PollVault/ Interval Estimator 95% Confidence Interval for p Standard Normal P(-1.96 ? z ? 1.96) =. 95 .9