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1ECON20003 Quantitative Methods 2 2ndSemester 2017 Solutions to Tutorial 3 Question A1 (a)Let μNOWand μBEFOREbe the population mean monthly mortgage payments now and five years ago, respectively. Step 1: The null and alternative hypotheses are 0:μμNOWBEFOREH=versus 1:μμNOWBEFOREH>The alternative hypothesis is the one that we wish to establish, namely, that mortgage payments have increased. Step 2: The test statistic and its sampling distribution when 0His true.The chosen test statistic depends on whether we assume the two population variances 2NOWand 2BEFOREare equal. With equal variances: (298)~11150150NOWBEFOREPXXtts-=+With unequal variances: (ν)22~150150NOWBEFORENOWBEFOREXXttss-=+where 222222122121114914922982NOWBEFORENOWBEFORENOWBEFOREpnsnssssssnn2222222150150150150149149NOWBEFORENOWBEFOREssss In Question C1 you are asked to show that both tstatistics are equal when the two sample sizes are equal. Their degrees of freedom could be different, however. Step 3:Level of significance: α0.05=. Step 4: The decision rule for equal variances is Reject H0if ()0.05, 2981.650tt>=(or if p-value < 0.05)
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