2007solutions - Solution to Mid-Term Quiz February 10, 2007...

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1 Solution to Mid-Term Quiz February 10, 2007 Qu.#1 (18 Marks) a. (4 Marks) You should use the “Matched-Pair” t-Test for Differences. [1 MARK] This is so because the 15 production workers are the same 15 production workers on both the days considered and during the same work-shifts and as such the samples are related and matched and the main issue is to check if there is a difference in the units produced [1 MARK]. The boxplot for the Difference in production is fairly symmetrical with no suspected or real outliers and therefore is reasonably normally distributed [1 MARK] and as such the Parametric Matched-pair t- Test IS the appropriate test for this situation. The non-Parametric analogue of the t-Test, the Wilcoxon test, is NOT appropriate. [1 MARK] b. (4 Marks) Testing if the Friday production has decreased is the same as testing if the Wednesday production is more. Manual Test: (Steps are used for Marking Convenience only!) Step#1: H 0 : d = 0 [1 MARK] H A : d > 0 Right Tailed for Convenience(Could be Left Tailed) Step#2: 0 ( ) ( ) 18.4667 0 18.4667 3.7711 18.9656 ( ) 4.8969 15 d Calc d t SE d μ - - = = = = [1 MARK] Step#3: t Crit = t ± (n-1) = t 0.05 (14) = 1.7613 Step#4: Since {t Calc = 3.7711} > {t Crit = t = t 0.05 = 1.7613} Reject H 0 . [1 MARK] {The Mean Value of Wednesday production IS more than the Mean Value of Friday production or equivalently, the Mean Value of Friday production has decreased from the Mean Value of the Wednesday production.}[1 MARK] Alternatively one can do the following equivalent Left Tailed Test: One-Sample T: -Differ (the negative difference) Test of mu = 0 vs < 0 95% Upper Variable N Mean StDev SE Mean Bound T P -Differ 15 -18.4667 18.9656 4.8969 -9.8417 -3.77 0.001 [ this approach will give the equivalent of the middle two marks above. Hypotheses and conclusion are still needed. ] c. (4 Marks) Note that we will also allow a "1 -sided" interval or upper bound, but not a lower bound.
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2 Since we want to work with the difference (in this case of Wed production - Fri production), [1 mark for statement of intent -- need to follow through with correct sign], we use the data above for the sample mean
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2007solutions - Solution to Mid-Term Quiz February 10, 2007...

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