Consider the following ANOVA experiments. (Give your answers correct to two decimal places.)
(a) Determine the critical region and critical value that are used in the classical approach for testing the null hypothesis Ho: ì1 = ì2 = ì3 = ì4, with n = 19 and á = 0.01.
F
(b) Determine the critical region and critical value that are used in the classical approach for testing the null hypothesis Ho: ì1 = ì2 = ì3 = ì4 = ì5, with n = 17 and á = 0.05.
F
(c) Determine the critical region and critical value that are used in the classical approach for testing the null hypothesis Ho: ì1 = ì2 = ì3, with n = 19 and á = 0.05.
F
this is the answers that I got and they were wrong. f>equal to 3.20 for a part and b part I got f>equal to 3.41 But they both are wrong do not thing I am sitting them up right, any help?
You will need to determine "degrees of freedom between" and "degrees of freedom within" before checking an ANOVA table using alpha level.
To calculate df between:
k - 1 = 3 - 1 = 2
Note: k = number of levels.
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To calculate df within:
N - k = 15 - 3 = 12
Note: N = total number of values in all levels.
Let's do part a) and see if you can work out the rest.
a) You have 4 levels. Your sample size is 19. Your alpha level is 0.01.
df between = k - 1 = 4 - 1 = 3
df within = N - k = 19 - 4 = 15
Checking the table using 0.01 alpha level using the above degrees of freedom, I see critical value of 5.42.
I'll let you try the rest.
Can you give me a site for the correct values, I must not be looking at the same one or I am looking at the wrong ones because I can not get the numbers to match to the one you done. I do appreciate all your help.
So this is what I came up with on (b) 6.93 and (c) 6.48 and those were wrong. I think I am missing them at the beginning when k-1=?-1 and n-k=?-?. Which graph or table are you getting these from? I figure out the other one to come up with the answers but I must of missed the first part.
To determine the critical region and critical value for the classical approach of testing a null hypothesis in ANOVA experiments, we need to first find the degrees of freedom for each of the hypotheses.
For part (a), we are testing the null hypothesis Ho: ì1 = ì2 = ì3 = ì4, with n = 19 and á = 0.01. The degrees of freedom for numerator (right-hand) is k - 1 = 4 - 1 = 3, where k is the number of groups. The degrees of freedom for denominator (left-hand) is n - k = 19 - 4 = 15.
To find the critical value, we need to consult the F-distribution table with a significance level of 0.01 and degrees of freedom (3, 15). Looking up the table, we find the critical value to be approximately 3.59.
The critical region for the classical approach is when the calculated F-statistic is greater than the critical value. So, if F > 3.59, we reject the null hypothesis.
For part (b), we are testing the null hypothesis Ho: ì1 = ì2 = ì3 = ì4 = ì5, with n = 17 and á = 0.05. The degrees of freedom for numerator (right-hand) is k - 1 = 5 - 1 = 4, and the degrees of freedom for denominator (left-hand) is n - k = 17 - 5 = 12.
Consulting the F-distribution table with a significance level of 0.05 and degrees of freedom (4, 12), we find the critical value to be approximately 3.49.
The critical region for the classical approach is when the calculated F-statistic is greater than the critical value. So, if F > 3.49, we reject the null hypothesis.
For part (c), we are testing the null hypothesis Ho: ì1 = ì2 = ì3, with n = 19 and á = 0.05. The degrees of freedom for numerator (right-hand) is k - 1 = 3 - 1 = 2, and the degrees of freedom for denominator (left-hand) is n - k = 19 - 3 = 16.
Consulting the F-distribution table with a significance level of 0.05 and degrees of freedom (2, 16), we find the critical value to be approximately 3.59.
The critical region for the classical approach is when the calculated F-statistic is greater than the critical value. So, if F > 3.59, we reject the null hypothesis.