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Unformatted text preview: STAT424 Spring 2010 Homework #4 Mar 17, 2010 Homework 4 Due: Tuesday, March 30, 2010 1) Circle the best answer. If you choose “None of the above”, please provide your correct answer. 1. A one-way ANOVA with three levels was conducted and the null hypothesis was rejected. The magnitude of sample means were: ¯ y 1 · < ¯ y 2 · < ¯ y 3 · . Larger means are considered better. Using this information alone, we can a) conclude that level 1 is worse than level 2. b) conclude that level 2 is the best. c) conclude that level 2 and 3 are better. d) None of the above. 2. A one-way ANOVA was conducted on a dataset with five levels. Sample sizes for each level were 5, 6, 5, 5, and 4. The correct degrees of freedoms for M A · , M ⊥ A and M ⊥ in the ANOVA table are: a) 5, 20, 25, respectively. b) 5, 19, 24, respectively. c) 4, 21, 25, respectively. d) 4, 20, 24, respectively. 3. A one-way ANOVA was conducted on a dataset with four levels. Sample sizes for each level were 5, 6, 5, and 4. The F statistic has which of the following distributions, when H is true? a) T 4 b) T 5 , 19 c) F 3 , 16 d) F 4 , 18 e) F 4 , 15 4. What is the appropriate model for a one-way ANOVA? a) y i = β + β 1 x i b) y i = β + β 1 x i + i , wehre i iid ∼ F ( g,n- g ), where g denotes the number of groups and n denotes the sample size. c) y ij = μ i + j , where j iid ∼ N (0 ,σ 2 ) d) y ij = μ i + ij , where j iid ∼ N (0 ,σ 2 ) e) None of the above. 5. When the null hypothesis is rejected for a one-way ANOVA, it means that: a) The variation between the groups is large relative to the variation within the groups. b) The variation between the groups is small relative to the variation within the groups. c) The variation within the groups is large relative to the variation among the groups. d) The variation within the groups is equal to the variation among the groups....
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- Spring '08
- Variance, Null hypothesis, Statistical hypothesis testing, Schutzstaffel