Question

Find, or come up with, a data set to test the equality of means of 3 categories. Provide the sample statistics for each category. Using technology (Ti-84 or Excel) find the critical value, test statistic and p-value of the ANOVA test. Then interpret the results in the context of the problem.

Answer 1

Sol:

let A,B,C represents 3 groups

A	B	C
20	47	17
23	49	25
25	67	17
27	64	31
27	49	16
21	67	17
26	51	19
23	70	16
21	54	21
26	60	24
31	49	20

Ho;All the three group means are equal

Ha:atleast one of the group means are differnt

alpha=0.05

perfom ANOVA one way in excel

data>data analysis>anova single factor we gt

Output:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
A	11	270	24.54545	10.87273
B	11	627	57	76.4
C	11	223	20.27273	22.21818
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	8874.97	2	4437.485	121.585	4.08E-15	3.31583
Within Groups	1094.909	30	36.49697
Total	9969.879	32

From Output

Test statistic,F=121.585

p vlaue=4.08E-15=0.0000

F critical=3.31583

F statistic>F critical

Reject Null hypothesis

Accept aletrnative Hypothesis

Conclusion:

There is no sufficient statistical evidence at 5 % level of signifcance to conclude that all the 3 group means are equal.