Let F =MSTr/MSE Be the Test Statistic in a Single-Factor $H _ { o }$

question 8

Essay

Let F =MSTr/MSE be the test statistic in a single-factor ANOVA problem involving four populations or treatments with a random sample of six observations from each one. When $H _ { o }$ is true and the four population or treatment distributions are all normal with the same variance $\sigma ^ { 2 }$ then F has an F distribution with degrees of freedom $v _ { 1 } =$$\underline{\quad\quad}$ and $v _ { 2 } =$$\underline{\quad\quad}$ With f denoting the computed value of F, the rejection region for level .05 test is __________.

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Definitions:

Unbiased Coin

A coin for which the probability of landing on heads or tails is equal, implying fair outcomes.

Discrete Random Variable

A variable that can take on a countable number of distinct values, often representing categories or counts.

Nonnegative Probabilities

Probabilities that are greater than or equal to zero, as negative probabilities do not exist in standard probability theory.

Discrete Random Variable

A variable that represents counts or whole number values, having distinct and separate values which result from a counting process.