Chapter 31 What Do Samples Tell Us?

Chapter 32 Thought Question 1 During a medical exam, the doctor measures your cholesterol two times. Do you think both measurements would be exactly the same? Why or why not?

Chapter 33 Thought Question 2 To estimate the percentage of all adults who have an internet connection in their homes, a properly chosen sample of 1100 adults across the U.S. was sampled, and 60% said “yes”. How close do you think that is to the percentage of the entire country who have an internet connection? Within 30%? 10%? 5%? 1%? Exactly the same?

Chapter 34 Sampling Terminology u Parameter –fixed, unknown number that describes the population u Statistic –known value calculated from a sample –a statistic is used to estimate a parameter u Bias –in repeated samples, the sample statistic consistently misses the population parameter in the same direction u Variability –different samples from the same population may yield different values of the sample statistic

Chapter 35 Bias and Variability Consider shooting arrows at a target: Bias means the archer systematically misses in the same direction. Variability means that the arrows are scattered.

Chapter 36 Sampling Strategy u To reduce bias, use random sampling u To reduce variability, use larger samples –estimates from random samples will be closer to the true values in the population if the samples are larger –how close will they be? v margin of error

Chapter 37 u The proportion of a population that has some outcome (“success”) is p. u The proportion of successes in a sample is measured by the sample proportion: Proportions “p-hat”

Chapter 38 u The amount by which the proportion obtained from the sample ( ) will differ from the true population proportion (p) rarely exceeds the margin of error. Margin of Error u Typical margin of error: 1/sqrt(n) –In 95% of surveys, the sample proportion will not differ from the population proportion by any more than the margin of error. (“95% confidence”) demo

Chapter 39 Case Study 62% say it should be guaranteed by the government same as in 2000, up 6 points from % say it is not the responsibility of the government Guaranteed Health Insurance in the U.S.? New York Times/CBS News Poll, January 2006

Chapter 310 How the Poll was Conducted This New York Times/CBS News poll was based on telephone interviews conducted January 20 through January 25, 2006 with 1,229 adults throughout the United States. The survey has a random sampling error of approx. ±3 percent. Case Study

Chapter 311 Conclusion (Confidence statement) For the proportion of the population who favor guaranteed health insurance, the sample proportion was =.62 (62%) and the margin of error was ±.03 (3%). We can then say that “we are 95% confident that the proportion of the population who favor guaranteed health insurance was between.59 and.65 (59% and 65%).” Case Study

Chapter 312 Key Concepts u Parameter versus Statistic u Bias and Variability u Margin of Error u Confidence Statements