Question

Consider the following table:

	SS	DF	MS	F
Among Treatments	?	3	930.54
Error			287.24
Total	6238.5	15

Step 1 of 8: Calculate the sum of squares among treatments. Please round your answer to two decimal places.

Step 2 of 8: Calculate the sum of squares of experimental error. Please round your answer to two decimal places.

Step 3 of 8: Calculate the degrees of freedom of experimental error.

Step 4 of 8: Calculate the F-value. Please round your answer to two decimal places.

Step 5 of 8: What is the sum of squares of sample means about the grand mean? Please round your answer to two decimal places.

Step 6 of 8: What is the variation of the individual measurements about their respective means? Please round your answer to two decimal places.

Step 7 of 8: What is the critical value of F at the 0.1 level? Please round your answer to four decimal places, if necessary.

Step 8 of 8: Is F significant at 0.10.1? (yes, no)

Answer 1

Step 1: Sum of squares among treatments is given by:

Step 2: Sum of squares of error is given by:

Step 3: Degrees of freedom of experimental error is:

Step 4: The F-value is given by:

Step 5: The sum of squares of sample means about the grand mean is Same as sum of squares among treatments, i.e., 2791.62

Step 6: The variation of the individual measurements about their respective means is same as the sum of squares of experimental error i.e., 3446.88

Step 7: The test statistics follow F_3,12 distribution and it is always a right tailed test. So, the critical value at 0.1 level is

Step 8:

Yes, F is significant. This is Because F-value is greater than the critical value and it is always a right tailed test.