Homework ReviewParameters and StatisticsBiasTypes of BiasExamples of BiasAssignmentAnswers to Even-numbered ProblemsThe Language of SamplingLecture 6Sections 2.1-2.4Robb T. KoetherHampden-Sydney CollegeFri, Sep 2, 2011Robb T. Koether (Hampden-Sydney College) The Language of Sampling Fri, Sep 2, 2011 1 / 31Outline1Homework Review2Parameters and Statistics3Bias4Types of Bias5Examples of Bias6Assignment7Answers to Even-numbered ProblemsRobb T. Koether (Hampden-Sydney College) The Language of Sampling Fri, Sep 2, 2011 2 / 31Outline1Homework Review2Parameters and Statistics3Bias4Types of Bias5Examples of Bias6Assignment7Answers to Even-numbered ProblemsRobb T. Koether (Hampden-Sydney College) The Language of Sampling Fri, Sep 2, 2011 3 / 31Homework ReviewPage 67, Problem 1.31Jaeyun 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 oppositesides show up more often then others.The two dice look identical and are mixed so she cannot knowwhich die is which.Robb T. Koether (Hampden-Sydney College) The Language of Sampling Fri, Sep 2, 2011 4 / 31Homework ReviewPage 67, Problem 1.31She decides to select one of the two dice and roll that die onetime.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 / 31Homework ReviewPage 67, Problem 1.31The following table provides the chances of each of the sixpossible outcomes for each die:Outcome Chance if Die A (fair) Chance if Die B (biased)1 1/6 3/102 1/6 2/103 1/6 2/104 1/6 1/105 1/6 1/106 1/6 1/10Robb T. Koether (Hampden-Sydney College) The Language of Sampling Fri, Sep 2, 2011 6 / 31Homework ReviewPage 67, Problem 1.31(a) Since observing smaller outcomes (fewer dots) is more likely underthe alternative hypothesis, the direction of extreme is (select one)to the left to the right in both directions can’t tellThe direction of extreme is to the left.(b) Jaeyun decides to use the following decision rule: Reject H0if sherolls a 1 (or less). Calculate α, the chance of a Type I error, and β,the chance of a Type II error.α =16, β =710.(c) Jaeyun performs the experiment and she rolls a 2. Calculate thep-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 / 31Homework ReviewPage 67, Problem 1.31(a) Since observing smaller outcomes (fewer dots) is more likely underthe alternative hypothesis, the direction of extreme is (select one)to the left to the right in both directions can’t tellThe direction of extreme is to the left.(b) Jaeyun decides to use the following decision rule: Reject H0if sherolls a 1 (or less). Calculate α, the chance of a Type I error, and β,the chance of a Type II error.α =16, β =710.(c) Jaeyun performs the experiment and she rolls a 2. Calculate thep-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 / 31Homework ReviewPage 67, Problem 1.31(a) Since observing smaller outcomes (fewer dots) is more likely underthe alternative hypothesis, the direction of extreme is (select one)to the left to the right in both directions can’t tellThe direction of extreme is to the left.(b) Jaeyun decides to use the following decision rule: Reject H0if sherolls a 1 (or less). Calculate α, the chance of a Type I error, and β,the chance of a Type II error.α =16, β =710.(c) Jaeyun performs the experiment and she rolls a 2. Calculate thep-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 / 31Homework ReviewPage 67, Problem 1.31(a) Since observing smaller outcomes (fewer dots) is more likely underthe alternative hypothesis, the direction of extreme is (select one)to the left to the right in both directions can’t tellThe direction of extreme is to the left.(b) Jaeyun decides to use the following decision rule: Reject H0if sherolls a 1 (or less). Calculate α, the chance of a Type I error, and β,the chance of a Type II error.α =16, β =710.(c) Jaeyun performs the experiment and she rolls a 2. Calculate thep-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 / 31Homework ReviewPage 67, Problem 1.31(a) Since observing smaller outcomes (fewer dots) is more likely underthe alternative hypothesis, the direction of extreme is (select one)to the left to the right in both directions can’t tellThe direction of extreme is to the left.(b) Jaeyun decides to use the following decision rule: Reject H0if sherolls a 1 (or less). Calculate α, the chance of a Type I error, and β,the chance of a Type II error.α =16, β =710.(c) Jaeyun performs the experiment and she rolls a 2. Calculate thep-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 / 31Homework ReviewPage 67, Problem 1.31(a) Since observing smaller outcomes (fewer dots) is more likely underthe alternative hypothesis, the direction of extreme is (select one)to the left to the right in both directions can’t tellThe direction of extreme is to the left.(b) Jaeyun decides to use the following decision rule: Reject H0if sherolls a 1 (or less). Calculate α, the chance of a Type I error, and β,the chance of a Type II error.α =16, β =710.(c) Jaeyun performs the experiment and she rolls a 2. Calculate thep-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 / 31Outline1Homework Review2Parameters and Statistics3Bias4Types of Bias5Examples of Bias6Assignment7Answers to Even-numbered ProblemsRobb T. Koether (Hampden-Sydney College) The Language of Sampling Fri, Sep 2, 2011 8 / 31The Language of SamplingDefinition (Population size)The population size is the number of members in the population. It isdenoted by the symbol N.Definition (Sample size)The sample size is the number of members in the sample. It isdenoted 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
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