STATISTICS â UNDERSTANDING HYPOTHESIS TESTS

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Statistics – Understanding Hypothesis Tests:Proportions201440. A 95% confidence interval is constructed for the difference between p ANZand p Westpac . For the purpose of calculating se pˆANZ- pˆ), the(Westpacsampling situation can be described as:(1) one sample of size 761, several response categories.(2) one sample of size 387, several response categories.(3) one sample of size 761, many yes/no items.(4) two independent samples of sizes 157 and 230.(5) one sample of size 387, many yes/no items.41. A 95% confidence interval for the difference p ANZ − p Westpac is(−0.014, 0.187).The best interpretation of this interval is:With 95% confidence, the percentage of bank customers, withANZ as their main bank, who would describe their relationshipwith ANZ as ‘Not Close’ is somewhere between:(1) 1.4% and 18.7% higher than the percentage of bank customers,with Westpac as their main bank, who would describe theirrelationship with Westpac as ‘Not Close’.(2) 1.4% lower and 18.7% higher than the percentage of bankcustomers, with Westpac as their main bank, who would describetheir relationship with Westpac as ‘Not Close’.(3) 1.4% and 18.7% lower than the percentage of bank customers,with Westpac as their main bank, who would describe theirrelationship with Westpac as ‘Not Close’.(4) 1.4% higher and 18.7% lower than the percentage of bankcustomers, with Westpac as their main bank, who would describetheir relationship with Westpac as ‘Not Close’.(5) −1.4% and 18.7%.Questions 42 and 43 refer to the following additional information.Consider only customers with ANZ as their main bank.Let:p Close be the proportion who would describe their relationship with ANZ aseither ‘Quite Close’ or ‘Very Close’© Libraries and Learning Services - Student Learning Services (Tā te Ākonga) Page 38 of 44The University of Auckland
Statistics – Understanding Hypothesis Tests:Proportions2014andp Perform be the proportion who would describe the ANZ performance as‘Good’ or ‘Excellent’.Information from Tables 10 and 11, page 37, is used to conduct a two-tailedt-test for no difference between p Close and p Perform .42. The formula for the standard error of the estimate, se pˆClose- pˆ), is:(Perform(1)(2)22pˆClosepˆ Perform157 157(ˆ p ˆ ) (ˆ ˆClose pPerform- pClose- p157Perform)2(3)(ˆ pClose pˆPerform)- (ˆ p157Close pˆPerform)2(4)(5)(1 - pˆ) (1 ˆ ) (ˆ ˆClose - pPerform- pClose- p157pˆ(1 ˆ ) ˆ (1 ˆClose- pClosepPerform- p157157PerformPerform))243. The expression for evaluating the test statistic for the null hypothesis,H 0 : p Close − p Perform = 0, is:pClose- pPerform(1)se pˆ) se(ˆp )(ClosePerform(2)(3)(4)(5)pˆse(ˆpCloseClosese(ˆppˆse(ˆppse pˆpˆ- pˆ- pˆCloseCloseCloseClose))Perform2Perform- pˆ)Perform- se(ˆp- pˆ se(ˆp- p- pˆPerformClose Perform(Close PerformPerformPerform)))2© Libraries and Learning Services - Student Learning Services (Tā te Ākonga) Page 39 of 44The University of Auckland
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STATISTICS â UNDERSTANDING HYPOTHESIS TESTS