The Language of Sampling Lecture 6 Sections 2 1 2 4 Robb T Koether Hampden Sydney College Fri Sep 2 2011 Robb T Koether Hampden Sydney College The Language of Sampling Fri Sep 2 2011 1 31 Outline 1 Homework Review 2 Parameters and Statistics 3 Bias 4 Types of Bias 5 Examples of Bias 6 Assignment 7 Answers to Even numbered Problems Robb T Koether Hampden Sydney College The Language of Sampling Fri Sep 2 2011 2 31 Outline 1 Homework Review 2 Parameters and Statistics 3 Bias 4 Types of Bias 5 Examples of Bias 6 Assignment 7 Answers to Even numbered Problems Robb T Koether Hampden Sydney College The Language of Sampling Fri Sep 2 2011 3 31 Homework Review 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 The two dice look identical and are mixed so she cannot know which die is which Robb T Koether Hampden Sydney College The Language of Sampling Fri Sep 2 2011 4 31 Homework Review 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 Robb T Koether Hampden Sydney College The Language of Sampling Fri Sep 2 2011 5 31 Homework Review Page 67 Problem 1 31 The following table provides the chances of each 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 Robb T Koether Hampden Sydney College Chance if Die B biased 3 10 2 10 2 10 1 10 1 10 1 10 The Language of Sampling Fri Sep 2 2011 6 31 Homework Review 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 Robb T Koether Hampden Sydney College in both directions The Language of Sampling can t tell Fri Sep 2 2011 7 31 Homework Review 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 The direction of extreme is to the left Robb T Koether Hampden Sydney College The Language of Sampling Fri Sep 2 2011 7 31 Homework Review 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 The direction of extreme is to the left 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 Robb T Koether Hampden Sydney College The Language of Sampling Fri Sep 2 2011 7 31 Homework Review 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 The direction of extreme is to the left 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 61 7 10 Robb T Koether Hampden Sydney College The Language of Sampling Fri Sep 2 2011 7 31 Homework Review 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 The direction of extreme is to the left 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 61 7 10 c Jaeyun performs the experiment and she rolls a 2 Calculate the p value and give her decision Robb T Koether Hampden Sydney College The Language of Sampling Fri Sep 2 2011 7 31 Homework Review 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 The direction of extreme is to the left 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 61 7 10 c Jaeyun performs the experiment and she rolls a 2 Calculate the p value and give her decision p value 26 She accepts H0 Robb T Koether Hampden Sydney College The Language of Sampling Fri Sep 2 2011 7 31 Outline 1 Homework Review 2 Parameters and Statistics 3 Bias 4 Types of Bias 5 Examples of Bias 6 Assignment 7 Answers to Even numbered Problems Robb T Koether Hampden Sydney College The Language of Sampling Fri Sep 2 2011 8 31 The Language of Sampling 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 Definition Unit or subject A unit or subject is a single member of the population Robb T Koether Hampden Sydney College The Language of Sampling Fri Sep 2 2011 9 31 The Language of Sampling Definition Parameter A parameter is a numerical characteristic of the population Definition Statistic A statistic is a numerical characteristic of a sample Robb T Koether Hampden Sydney College The Language of Sampling Fri Sep 2 2011 10 31 The Language of Sampling 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 President Obama s performance is used to estimate the proportion of the population who approve of his performance Robb T Koether Hampden Sydney College The Language of Sampling Fri Sep 2 2011 11 31 The Language of Sampling Definition Variable A variable is a characteristic of individual members of the population 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 …
View Full Document
Unlocking...