Class Notes (834,526)
Tony Quon (67)
Lecture 7

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Tony Quon
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—> There is good evidence that the avg. bill in Munic. II exceeds \$80 1) H : µ − µ = 0 e.g, Is there evidence of a difference in avg. monthly bills? 0 1 2 H : µ − µ ≠ 0 a 1 2 2) α = 0.05 df = 40.13 3) UnequalVariance version: (x1− x 2−0 115−98 4) To determine whether to reject, we need to look at the tstat 2 2 = 2 2 = 2.37 s1 s2 30 18 row in the t-table with 40 degrees of freedom + + n 1 n 2 25 21 t.01,40= 2.423> t stat> t.025,40= 2.021 ⇒ 2×.01< P− value< 2×.025 —> There is evidence at the 5% signiﬁcance level of a difference in avg. monthly bills between municipalities 3) EqualVarianceversion: 2 2 2 2 2 (n1−1)s1+(n −2)s 2 (25−1)30 +(21−1)18 sp= = = 638.2 n1+ n2−2 25+ 21−2 s = 25.26 p (x1− x2)−0 115−98 stat = = 2.2 1 1 1 1 sp n +n 25.26 25 + 21 1 2 4) To determine whether to reject, we need to look at the row in the t-table with .01.402.423> tstat .025,402.021 44 degrees of freedom. However, the text only gives rows for d.f. 40 and 45 ⇒ 2×.01< P−value< 2×.025 —> In this case the conclusion in both the pooled and the unpooled version was to reject the null so…. —> There is evidence at the 5% signiﬁcance level of a difference in avg. monthly bills between municipalities Non-independent Populations: Subjec “Before” “After” Differenc Matched Pairs t-Test: t e —> Two linked measurements - i.e. “before” and “after” 1 … … d1 2 … … d2 3 … … d3 … … … … n … … d n Method: H0:µd= 0 Teststatisticstat d −0 —> Compute the mean and SD of the differences and perform a one sd/ n H :µ ≠ 0 (or >,stat e.g, Learning Evaluation or rejec0 H stattα/2,n-1stat −α/2,n-1 Subjec Pre-test Post-test Post-Pre t 1 30 29 -1 d =1.45 2 28 30 2
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