Homework ReviewParameters and StatisticsBiasTypes of BiasExamples of BiasAssignmentAnswers to Even-numbered ProblemsThe Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsThe Language of SamplingLecture 6Sections 2.1-2.4Robb T. KoetherHampden-Sydney CollegeFri, Sep 4, 2009The Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsOutline1Homework Review2Parameters and Statistics3Bias4Types of Bias5Examples of Bias6Assignment7Answers to Even-numbered ProblemsThe Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsHomework ReviewPage 67, Problem 1.31Jaeyun has two dice.Die A is a fair die; each of the six outcomes is equallylikely.Die B is biased–that is, it is heavier on some sides sothe opposite sides show up more often then others.The two dice look identical and are mixed so shecannot know which die is which.The Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsHomework ReviewPage 67, Problem 1.31She decides to select one of the two dice and roll thatdie one time.Based on the outcome, she must determine which die itis.That is, she must test the following hypotheses:H0: The selected die is Die A (fair).H1: The selected die is Die B (biased).The Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsHomework ReviewPage 67, Problem 1.31The following table provides the chances o feach of thesix possible 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 1/10The Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsHomework ReviewPage 67, Problem 1.31(a) Since observing smaller outcomes (fewer dots) is morelikely under the alternative hypothesis, the direction ofextreme 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 H0if she rolls a 1 (or less). Calculate α, thechance of a Type I error, and β, the chance of a Type IIerror.(c) Jaeyun performs the experiment and she rolls a 2.Calculate the p-value and give her decision.The Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsHomework ReviewSolution(a) The direction of extreme is to the left.(b) α =16, β =710.(c) p-value =26. She accepts H0.The Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsThe Language of SamplingDefinition (Population size)The population size is the number of members in thepopulation. It is denoted by the symbol N.Definition (Sample size)The sample size is the number of members in the sample. Itis denoted by the symbol n.Definition (Unit or subject)A unit or subject is a single member of the population.The Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsThe Language of SamplingDefinition (Parameter)A parameter is a numerical characteristic of the population.Definition (Statistic)A statistic is a numerical characteristic of a sample.The Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsThe Language of SamplingThe purpose of a statistic is to estimate thecorresponding parameter.For example,The average salary of a sample is used to estimate theaverage salary of the population.The proportion of a sample who approve of Obama isused to estimate the proportion of the population whoapprove of Obama.The Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsThe Language of SamplingDefinition (Variable)A variable is a characteristic of individual members of thepopulation.The data consist of the observed values of the variable.Definition (Sampling Error)The sampling error is the difference between the value of astatistic and the value of the parameter it was meant toestimate.The Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsParameters and StatisticsFor numerical data, we usually use the average of thevalues in the sample.For non-numerical data, we usually use the proportionof observations in a specific category.The Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsParameters and StatisticsExample (Averages and Proportions)In the study of the infant boys and girls, what was thevariable?Was it numerical or non-numerical?Which do you think the researchers used: an averageor a proportion?The Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsParameters and StatisticsExample (Averages and Proportions)In the coin-tossing experiment, what was the variable?Was it numerical or non-numerical?Which do I use: an average or a proportion?The Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsRandom vs. RepresentativeDefinition (Random sample)A random sample is a sample that is selected using aprocedure at least one step of which is left to chance.Definition (Representative sample)A representative sample is a sample that has all the samecharacteristics (except size) as the population from which itwas taken.The Languageof SamplingRobb T.KoetherHomeworkReviewParametersand StatisticsBiasTypes of BiasExamples ofBiasAssignmentAnswers toEven-numberedProblemsBiased SamplesDefinition (Biased sampling method)A sampling method is biased if it systematically produces asample whose characteristics differ from those of thepopulation.Definition (Biased sample)A sample is biased if was selected by a biased
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