11/29/2014 Parameter - In statistical practice, the value of a parameter is not known because we cannot examine the entire population. Statistic –In practice, we often use a statistic to estimate an unknown parameter. Sec 7.1: What is a Sampling Distribution Identify bold number as either a parameter or statistic 1. On Tuesday, the bottles of Arizona Iced Tea filled in a plant were supposed to contain an average of 20 ounces of iced tea. Quality control inspectors sampled 50 bottles at random from the day’s production. These bottles contained an average of 19.6 ounces of iced tea. 2. On a New York –to-Denver flight, 8% of the 125 passengers were selected for random security screening before boarding. According to TSA, 10% of passengers at this airport are chosen for random screening. Identify the population, the parameter, the sample, and the statistic in the following: a) A pediatrician wants to know the 75th percentile for the distribution of heights of 10-year-old boys so she takes a sample of 50 patients and calculates Q3 = 56 inches. b)A Pew Research Center Poll asked 1102 12- to 17year-olds in the United States if they have a cell phone. Of the respondents, 71% said Yes. Sampling Variability Sampling distribution • describes how a statistic varies in many samples from the population. • should be centered at the population parameter. • ideal pattern if we could look at all samples that size Population distribution Do CYU pg 420. 1 11/29/2014 What should we use to describe a sampling distribution? Unbiased estimator “unbiased” does not mean perfect. It will almost always provide an estimate that is not equal to the value of the population parameter. In many samples, it won’t consistently be too high or consistently too low. We are assuming that the sampling process we are using has no bias (sampling or nonsampling errors) Larger random samples give us more precise estimates of the parameter than smaller random samples. Variability of a statistic • Larger samples give smaller spread. *Divide by (n-1) to reduce bias when calculating sample variance (make it a better estimate of population variance. • The spread of the sampling distribution does not depend on the size of the population, as long as the population is at least 10 times larger than the sample. • Do CYU pg 426 Taking a larger sample doesn’t fix bias. Remember that even a very large voluntary response sample or convenience sample is worthless because of bias. Look at #19 pg430. HW: pg 428: 2, 5, 7, 9, 13, 21-24 2