The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Bias The Language of Sampling Lecture 6 Sections 2 1 2 4 Types of Bias Examples of Bias Robb T Koether Assignment Answers to Evennumbered Problems Hampden Sydney College Fri Sep 4 2009 Outline The Language of Sampling Robb T Koether 1 Homework Review Homework Review 2 Parameters and Statistics 3 Bias 4 Types of Bias Assignment 5 Examples of Bias Answers to Evennumbered Problems 6 Assignment 7 Answers to Even numbered Problems Parameters and Statistics Bias Types of Bias Examples of Bias Homework Review The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Bias Types of Bias Examples of Bias Page 67 Problem 1 31 Jaeyun has two dice Die A is a fair die each of the six outcomes is equally likely Die B is biased that is it is heavier on some sides so the opposite sides show up more often then others Assignment Answers to Evennumbered Problems The two dice look identical and are mixed so she cannot know which die is which Homework Review The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Bias Types of Bias Examples of Bias Assignment Answers to Evennumbered Problems Page 67 Problem 1 31 She decides to select one of the two dice and roll that die one time Based on the outcome she must determine which die it is That is she must test the following hypotheses H0 The selected die is Die A fair H1 The selected die is Die B biased Homework Review The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Bias Types of Bias Examples of Bias Assignment Answers to Evennumbered Problems Page 67 Problem 1 31 The following table provides the chances o feach of the six possible outcomes for each die Outcome 1 2 3 4 5 6 Chance if Die A fair 1 6 1 6 1 6 1 6 1 6 1 6 Chance if Die B biased 3 10 2 10 2 10 1 10 1 10 1 10 Homework Review The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Bias Types of Bias Examples of Bias Assignment Answers to Evennumbered Problems Page 67 Problem 1 31 a Since observing smaller outcomes fewer dots is more likely under the alternative hypothesis the direction of extreme is select one to the left to the right in both directions can t tell b Jaeyun decides to use the following decision rule Reject H0 if she rolls a 1 or less Calculate the chance of a Type I error and the chance of a Type II error c Jaeyun performs the experiment and she rolls a 2 Calculate the p value and give her decision Homework Review The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Bias Solution a The direction of extreme is to the left Types of Bias b 16 Examples of Bias c p value 26 She accepts H0 Assignment Answers to Evennumbered Problems 7 10 The Language of Sampling The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Bias Types of Bias Examples of Bias Definition Population size The population size is the number of members in the population It is denoted by the symbol N Definition Sample size The sample size is the number of members in the sample It is denoted by the symbol n Assignment Answers to Evennumbered Problems Definition Unit or subject A unit or subject is a single member of the population The Language of Sampling The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Bias Definition Parameter A parameter is a numerical characteristic of the population Types of Bias Examples of Bias Assignment Answers to Evennumbered Problems Definition Statistic A statistic is a numerical characteristic of a sample The Language of Sampling The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Bias Types of Bias Examples of Bias Assignment Answers to Evennumbered Problems The purpose of a statistic is to estimate the corresponding parameter For example The average salary of a sample is used to estimate the average salary of the population The proportion of a sample who approve of Obama is used to estimate the proportion of the population who approve of Obama The Language of Sampling The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Definition Variable A variable is a characteristic of individual members of the population Bias Types of Bias Examples of Bias Assignment Answers to Evennumbered Problems The data consist of the observed values of the variable Definition Sampling Error The sampling error is the difference between the value of a statistic and the value of the parameter it was meant to estimate Parameters and Statistics The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Bias Types of Bias Examples of Bias Assignment Answers to Evennumbered Problems For numerical data we usually use the average of the values in the sample For non numerical data we usually use the proportion of observations in a specific category Parameters and Statistics The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Bias Types of Bias Examples of Bias Assignment Answers to Evennumbered Problems Example Averages and Proportions In the study of the infant boys and girls what was the variable Was it numerical or non numerical Which do you think the researchers used an average or a proportion Parameters and Statistics The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Example Averages and Proportions Bias In the coin tossing experiment what was the variable Types of Bias Was it numerical or non numerical Examples of Bias Which do I use an average or a proportion Assignment Answers to Evennumbered Problems Random vs Representative The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Definition Random sample A random sample is a sample that is selected using a procedure at least one step of which is left to chance Bias Types of Bias Examples of Bias Assignment Answers to Evennumbered Problems Definition Representative sample A representative sample is a sample that has all the same characteristics except size as the population from which it was taken Biased Samples The Language of Sampling Robb T Koether Homework Review Parameters and Statistics Bias Definition Biased sampling method A sampling method is biased if it systematically produces a sample whose characteristics differ from those of the population Types of Bias Examples of Bias Assignment Answers to
View Full Document
Unlocking...