Homework ReviewIntroductionTI-83 Data OptionStudent's t DistributionDegrees of Freedomt ProbabilitiesHypothesis Testing ( Unknown)AssignmentStudent’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentStudent’s t DistributionLecture 34Section 10.2Robb T. KoetherHampden-Sydney CollegeFri, Oct 30, 2009Student’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentOutline1Homework Review2Introduction3TI-83 Data Option4Student’s t Distribution5Degrees of Freedom6t Probabilities7Hypothesis Testing (σ Unknown)8AssignmentStudent’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentOutline1Homework Review2Introduction3TI-83 Data Option4Student’s t Distribution5Degrees of Freedom6t Probabilities7Hypothesis Testing (σ Unknown)8AssignmentStudent’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentHomework ReviewExercise 10.4, page 633.A psychologist is studying the distribution of IQ scoresof girls at an alternative high school.She wants to test the hypothesis that the average IQscore is 100 against the alternative that it is higher than100.She assumes that the normal distribution with standarddeviation 15 is a good model for these IQ scores.She takes a random sample of nine girls from this highschool and measures their IQ.The average IQ score for these nine girls was 114.Student’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentHomework ReviewExercise 10.4, page 633.Assuming that the appropriate assumptions are met,compute the test statistic and p-value for this test.State your decision at level α = 0.01 and write up yourconclusion in words.Student’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentHomework ReviewSolutionLet’s just show all seven steps.(1) The hypotheses areH0: µ = 100.H1: µ > 100.(2) α = 0.01.(3) The test statistic is z =x − µ0σ/√n.Student’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentHomework ReviewSolution(4) Compute z =114−10015/√9=145= 2.8.(5) The p-value is normalcdf(2.8,E99) = 0.0026.(6) Reject H0.(7) The average IQ score of the girls at the alternative highschool is higher than 100.Student’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentOutline1Homework Review2Introduction3TI-83 Data Option4Student’s t Distribution5Degrees of Freedom6t Probabilities7Hypothesis Testing (σ Unknown)8AssignmentStudent’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentIntroductionLast time, we made a very important, but unrealistic,assumption: The value of σ was known.What happens if σ is not known?We have to use s as an approximate the value of σ.Does that have any ramifications?Yes!But first, let’s do the Z-test on the TI-83 using the dataoption.Student’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentIntroductionLast time, we made a very important, but unrealistic,assumption: The value of σ was known.What happens if σ is not known?We have to use s as an approximate the value of σ.Does that have any ramifications?Yes!But first, let’s do the Z-test on the TI-83 using the dataoption.Student’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentIntroductionLast time, we made a very important, but unrealistic,assumption: The value of σ was known.What happens if σ is not known?We have to use s as an approximate the value of σ.Does that have any ramifications?Yes!But first, let’s do the Z-test on the TI-83 using the dataoption.Student’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentIntroductionLast time, we made a very important, but unrealistic,assumption: The value of σ was known.What happens if σ is not known?We have to use s as an approximate the value of σ.Does that have any ramifications?Yes!But first, let’s do the Z-test on the TI-83 using the dataoption.Student’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentIntroductionLast time, we made a very important, but unrealistic,assumption: The value of σ was known.What happens if σ is not known?We have to use s as an approximate the value of σ.Does that have any ramifications?Yes!But first, let’s do the Z-test on the TI-83 using the dataoption.Student’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentIntroductionLast time, we made a very important, but unrealistic,assumption: The value of σ was known.What happens if σ is not known?We have to use s as an approximate the value of σ.Does that have any ramifications?Yes!But first, let’s do the Z-test on the TI-83 using the dataoption.Student’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt ProbabilitiesHypothesisTesting (σUnknown)AssignmentOutline1Homework Review2Introduction3TI-83 Data Option4Student’s t Distribution5Degrees of Freedom6t Probabilities7Hypothesis Testing (σ Unknown)8AssignmentStudent’s tDistributionRobb T.KoetherHomeworkReviewIntroductionTI-83 DataOptionStudent’s tDistributionDegrees ofFreedomt
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