Question

Consider the following table:

	SS	DF	MS	F
Among Treatments	2580.06		368.58	0.95
Error
Total	7601.31	20

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 0.01 level? Please round your answer to four decimal places, if necessary.

Step 8 of 8: Is F significant at 0.01? Yes or No?

Answer 1

This is a one way ANOVA testing.

This is ANOVA - Single Factor. We first need to find the and . They are 'Total variance' and 'Variance in between the treatments' respectively.

We know

= 7601.31 - 2580.06

= 5021.25

For the df we have

MSB = SS_b / df_b

df_b = SS_b/ MSB

=2580.06 /368.58

=7

df(total) = df(bet) + df(within)

20 =7 +df(within)

df(within) =20 - 7

=13

MSE = 5021.25 / 13

Test Stat = MSB / MSE

= 0.95

	SS	df	MS (SS /df)	F-stat
Between / among	2580.06	7	368.58	0.95
within/error	5021.25	13	386.25
Total	7601.31	20

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.

This is the sum of squares between

SSB = 2580.06

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

This is the sum of squares within

SSE = 5021.25

Step 7 of 8: What is the critical value of F at the 0.01 level? Please round your answer to four decimal places, if necessary.

critical value at 1%

C.V. =

= F_{7, 13, 0.01}

= 4.441 .......................found using f-dist tables with df1 = 7 df2= 13 and p =0.01

Step 8 of 8: Is F significant at 0.01? Yes or No?

Since Test Stat (0.95) < C.V.

We do not reject the null hypothesis at 1% level.

Ans: F significant at 0.01 : No