Spring 2004



Which Test?a) test of independenceb) other test…we can only use on individual counts, rather than averages.c) test of homogeneityd) GOFe) other test… we can only use to test relationships between categorical variablesf) test of independencePi. HypothesisWe want to know whether the first million digits of π are uniformly distributed.Ho: Digits of π are uniformly distributed.Ha: Digits of π are NOT uniformly distributed.PlanCounted data condition: We have counts of the digits.Randomization condition: We expect the digits of π to be random since it is an irrational number.Expected cell frequency: The null hypothesis expected 10% or 100,000 of each digit to appear in the first million digits. (Definitely greater than 5.)We will do a χ2 goodness-of-fit test. The sampling distribution of the test statistic is χ2 with 10 – 1 = 9 degrees of freedom.MechanicsThe expected value for each digit is 10% of 1,000,000 or 100,000.The P-value is the area in the upper tail of the χ2 model for 9 degrees of freedom above the computed χ2 value.ConclusionThe P-value is large. We fail to reject the null hypothesis.These data provide no evidence that the digits of π are not uniformly distributed.Montana. HypothesisWe want to know whether political affiliation is independent of gender.Ho: Political affiliation is independent of gender.Ha: There is a relationship between political affiliation and gender.PlanCounted data condition: We have counts.Randomization condition: random survey but not extendible to other states.Expected cell frequency: All expected frequencies > 5 (check after test).We will do a χ2 test for independence. The sampling distribution of the test statistic is χ2 with degrees of freedom.MechanicsEnter the data in table above into matrix A of the calculator. Perform a χ2 test.The test reports .The P-value is the area in the upper tail of the χ2 model for 2 degrees of freedom above the computed χ2 value.ConclusionAssuming α =.05, the P-value is relatively large (greater than 0.05). We fail to reject the null hypothesis.These data provide tentative evidence that there is no relationship between political affiliation and gender.Mileage. You cannot perform a χ2 statistical test for this data because we do not have counts. We have instead average number of miles driven per week.Pregnancies. HypothesisWe want to know whether pregnancy outcome depends on the age of the mother.Ho: Pregnancy outcome is independent of mother’s age.Ha: There is a relationship between pregnancy outcome and mother’s age.PlanCounted data condition: We have counts.Randomization condition: assume random sample of U.S. population.Expected cell frequency: All expected frequencies > 5 (check after test).We will do a χ2 test for independence. The sampling distribution of the test statistic is χ2 with degrees of freedom.MechanicsEnter the data in table above into matrix A of the calculator. Perform a χ2 test.The test reports .The P-value is the area in the upper tail of the χ2 model for 3 degrees of freedom above the computed χ2 value.ConclusionThe P-value is relatively high (P > 0.1). We fail to reject the null hypothesis.These data show no evidence of a relationship between pregnancy outcome and the age of the mother. ................
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