In a completely randomized design, ten subjects were assigned to each of four tr
ID: 3263618 • Letter: I
Question
In a completely randomized design, ten subjects were assigned to each of four treatments of a factor. The partially completed ANOVA table is shown below. Complete parts a through d. a) What are the degrees of freedom for treatment, error, and total? The degrees of freedom for treatment are ___________. (Simplify your answer.) The degrees of freedom for error are ____________. (Simplify your answer.) The degrees of freedom for the total are ______________. (Simplify your answer.) b) What is SSE? SSE = ____________ (Type an integer or a decimal.) c) What is MSTr? MSTr = ____________ (Round to two decimal places as needed.) d) What is MSE? MSE = __________. (Round to two decimal places as needed.) Is the following statement true or false? If false, explain briefly. Using an alpha level of 0.01, a P-value of 0.06 means the null hypothesis is true. Choose the correct answer below. A. The statement is false because this P-value only means that there is not enough evidence to reject the null hypothesis. B. The statement is false because this P-value means that the null hypothesis is false. C. The statement is false because the P-value would have to be less than 0.01 to state that the null hypothesis is true. D. The statement is true.Explanation / Answer
(a) The degrees of freedom for treatment are : c - 1 = 4 - 1 = 3
The degees of freedpm for error are: N - c
Here, N = 4 X 10 = 40
c = 4
So, The number of degrees of freedpm for error are : 40 - 4 = 36
The degrees of freedpm for total are: N - 1 = 40 - 1 = 39
(b ) SSE = SST - SSC = 1131.88 - 835.04 = 296.84
MSTr = 835.04/3 = 278.35
MSE = 296.84/36 =8.2456
Correct option:
A. The statement is false because this P - value only means that there is not enough evidence to reject the null hypothesis.