Question

Below you will find the null and alternative hypothesis for an ANOVA:

H0: μ1 = μ2 = μ3

H1: at least one of the means is different.

For Data Set B, based on the p-value and F vs. F critical values we found above, do we fail to reject the null hypothesis? Or, do we reject the null hypothesis?

Group of answer choices

Fail to Reject

Reject

Using Data Set B, run the Single Factor ANOVA in Excel, as we did in class. What p-value did you get?

Data Set B:

Math	History	Oceanography
43	66	31
53	54	40
49	58	53
54	64	42
43	64	51
43	64	38
45	56	55
51	55	46
54	54	40

Group of answer choices

0.48

1.48

0.000048

0.0048

U

sing Data Set B, what F and F critical values did you get?

Math	History	Oceanography
43	66	31
53	54	40
49	58	53
54	64	42
43	64	51
43	64	38
45	56	55
51	55	46
54	54	40

Group of answer choices

12.12; 4.28

15.50; 3.40

30; 15.30

2.33; 9.38

Answer 1

Here we perform Anova usin excel

So we have to test

H0: μ1 = μ2 = μ3

H1: at least one of the means is different.

So after doing Anova in excel we get the output

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Math	9	435	48.33333	23.75
History	9	535	59.44444	24.77778
Oceanography	9	396	44	62
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1142.296	2	571.1481	15.50239	0.000048	3.402826
Within Groups	884.2222	24	36.84259
Total	2026.519	26

So we get the P-value = 0.000048

So here we assume that level of significance = 0.05

Now we have P-value = 0.000048 < = 0.05 so we reject the null hypothesis and conclude that at least one of the means is different.

2)

F and F critical values

So from above output we have

F=15.50

F critical = 3.40

So here F=15.50 > F critical = 3.40 so we reject the null hypothesis and conclude that at least one of the means is different , 0,05 level of significance.