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STA2020F TEST 1 SOLUTIONS

# STA2020F TEST 1 SOLUTIONS - STA2020F 2007 CLASS TEST 1...

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STA2020F 2007 CLASS TEST 1 SOLUTIONS SECTION A: 1. T 2. F 3. T 4. T 5. T 6. T 7. T 8. F [1 x 8 = 8] SECTION B: Question 1: [13] a. Two factor anova with interaction or two factor factorial experiment [1] b. Variation due to differences in room sizes (density) [2]; Variation due to differences in behaviour (Comments) [2]; Variation due to interaction between behaviour (Comments) [2] and room sizes (Density) [2]; Variation due to error [2]; Total Variation [2]. c. (i) Separate studies cannot reveal interaction between the two factors [1] (ii) A factorial design is economical in that in a single experiment one can study the effects of the main factors and that of interaction. [1] Question 2: [12] a. 0 1 2 3 : H μ μ μ = = 1 H : at least 2 means differ (2) b. Source of Variation SS df MS F F critical Treatments 36.4 2 18.2 5.2 3.89 Error 42.0 12 3.5 Total 78.4 14 (8) c. Test statistic: F = 5.2; Critical value, F 2, 12 = 3.89. Since F = 5.2 > 3.89, reject 0 H . Therefore at least two of the population means differ. (2)

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Question 3. [12] (a) Complete 3 x 3 factorial experiment. [1] (b) SS(AB) measures the variability in share price between combinations (interactions) of the levels of the two factors. [2] (c) (i) H 0 : The levels of the two factors do NOT interact to affect the mean share price H 1 : The levels of the two factors interact to affect the mean share price [1] F STAT = 1.8898 P-value = 0.1202 Since the p-value of 0.1202 > 0.05, we do NOT reject H
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