STATISTICS – UNDERSTANDING HYPOTHESIS TESTS

Questions 4 to 6 refer to the following information.Statistics – Understanding Hypothesis Tests:Proportions2014Death Penalty Survey Results“Should convicted murderersbe put to death?”AustraliaN.Z.Yes 46% 42%No 39% 41%Can’t Say 15% 17%[Polls of 1307 Australians & 1010 New Zealanders]4. Based on previous studies, a researcher believes that the proportion of NewZealanders who agree that convicted murderers should be put to deathwould be more than forty percent. The hypotheses for this test would be:(1) H 0 : p = 0.40; H 1 : p 0.40(2) H 0 : p < 0.40; H 1 : p = 0.40(3) H 0 : p = 0.40; H 1 : p > 0.40(4) H 0 : p < 0.40; H 1 : p 0.40(5) H 0 : p < 0.40; H 1 : p > 0.405. Let’s assume instead that the researcher tested H 0 : p = 0.40 versusH 1 : p 0.40 where p = the proportion of New Zealanders who agree thatconvicted murderers should be put to death. The value of the t-teststatistic, t 0 , and the degrees of freedom df, to be used with 95% confidenceare given by:(1) t 0 = 1.288, df = ∞(4) t 0 = 1.288, df = 1.96(2) t 0 = 1.288, df = 1009(5) t 0 = -1.288, df = 1009(3) t 0 = -1.288, df = ∞Another difference considered by the researcher was between the proportion ofAustralians supporting the death penalty for convicted murderers and the proportionof New Zealanders supporting the death penalty for convicted murderers.6. To test for a difference in the two proportions given above the hypotheseswould be:(1) H0: μ1 μ2 0 vs H1: μ1 μ2 0(2) H : ˆ ˆ0p1 p2 0 vs H : ˆ ˆ1p1 p2 0(3) H0: p1 p2 0 vs H1: p1 p2 0(4) H : ˆ ˆ0p1 p2 0 vs H : ˆ ˆ1p1 p2 0(5) H p p 0 vs H p p 00:1 21:1 2© Libraries and Learning Services - Student Learning Services (Tā te Ākonga) Page 22 of 44The University of Auckland