Tutorial 3 solutions.pdf - ECON20003 Quantitative Methods 2...

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1 ECON20003 Quantitative Methods 2 2 nd Semester 2017 Solutions to Tutorial 3 Question A1 (a) Let μ NOW and μ BEFORE be the population mean monthly mortgage payments now and five years ago, respectively. Step 1: The null and alternative hypotheses are 0 : μ μ NOW BEFORE H = versus 1 : μ μ NOW BEFORE H > 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 0 H is true . The chosen test statistic depends on whether we assume the two population variances 2 NOW and 2 BEFORE are equal. With equal variances: (298) ~ 1 1 150 150 NOW BEFORE P X X t t s - = + With unequal variances: ( ν ) 2 2 ~ 150 150 NOW BEFORE NOW BEFORE X X t t s s - = + where 2 2 2 2 2 2 1 2 2 1 2 1 1 149 149 2 298 2 NOW BEFORE NOW BEFORE NOW BEFORE p n s n s s s s s s n n 2 2 2 2 2 2 2 150 150 150 150 149 149 NOW BEFORE NOW BEFORE s s s s   In Question C1 you are asked to show that both t statistics are equal when the two sample sizes are equal. Their degrees of freedom could be different, however. Step 3: Level of significance: α 0.05 = . Step 4: The decision rule for equal variances is Reject H 0 if ( ) 0.05, 298 1.650 t t > = (or if p -value < 0.05)
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