Question

Fifteen people were randomly selected from the population and randomly assigned to 1 of 3 experimental groups. Group 3 was included as the control group and did not receive any treatment. Use the following data set to answer the questions.

Group 1	Group 2	Group 3
21	25	32
53	54	41
44	26	86
72	32	75

Is there a significant difference (α=0.05) between at least two groups?  

	A.	Yes
	B.	No
	C.	Not possible to determine
	D.	Alpha level is incorrect

Answer 1

Answer:

B. No

Explanation:
Hypothesis:Here to check significant difference , we use one way ANOVA .

H0: All the groups are same

H1: There a significant difference between at least two groups.

To find ANOVA we use Excel:

First enter the data into excel

Group1	Group2	Group3
21	25	32
53	54	41
44	26	86
72	32	75

Go to Data> data analysis > ANOVA single factor > Give input range of all data > give output range > OK

The excel output is :

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Group1	4	190	47.5	448.3333
Group2	4	137	34.25	182.9167
Group3	4	234	58.5	679
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	1179.5	2	589.75	1.350315	0.307008	4.256495
Within Groups	3930.75	9	436.75
Total	5110.25	11

Decision :

We reject H0 if the p-value is less than significant difference (α=0.05) . But here P-value = 0.307008 > α=0.05, hence we can not reject H0. Therefore we conclude that All the groups are same. That means there 'no' significant difference (α=0.05) between at least two groups.