Samples Were Drawn from Three Populations $\bar { x } _ { 1 } = 1.71 , \bar { x } _ { 2 } = 1.95$

question 26

Short Answer

Samples were drawn from three populations. The sample sizes were n₁=8, n₂=8, and n₃=7 . The sample means were $\bar { x } _ { 1 } = 1.71 , \bar { x } _ { 2 } = 1.95$ , and $\bar { x } _ { 3 }$ =2.57 . The sample standard deviations were s₁=0.27, s₂=0.45, and s₃=0.25 . The grand mean is =2.055217.
i). Compute the sums of squares SSTr and SSE.
ii). How many degrees of freedom are there for SSTr and SSE?
iii). Compute the sums of squares MSTr and MSE.
iv). Compute the value of the test statistic F.
v). Can you conclude that two or more of the population means are different? Use the $\alpha = 0.05$ level of
significance.

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Definitions:

Emotions

Complex psychological states that involve physical arousal, expressive behaviors, and conscious experience.

Feelings

Emotional states or reactions that are subjectively experienced as pleasant or unpleasant sensations.

Social Conventions

Rules, norms, or standards that govern behaviors within a society or group, often unwritten and learned through social interaction.

Hegel

German philosopher known for his dialectical method and his contributions to metaphysics, morality, historiography, and the philosophy of history, art, and religion.