Question

A Health Club chain offers three physical fitness programs in two states, New York and New Jersey. A researcher has decided to test the club’s advertised claims of the benefits of these programs. The table below, shows the results (weight loss in pounds) of the researcher’s findings.

States	SQ	PQ	TQ
New York	19	8	21
	18	10	31
	25	10	26
	20	18	28
	17	7	14
	21	16	24
New Jersey	15	23	31
	28	32	31
	17	26	26
	14	16	20
	17	27	14
	13	18	9

a) State the hypotheses for this experiment.

b) Using Excel, run the appropriate Data Analysis (Attach your Excel results)

c) Is there any significant interaction effect?

If there is any interaction effect? ___ Yes ___No. Explain why or, why: not.

d) Make your decision(s): (

e) Draw your conclusion(s) (in the context of the problem):

Answer 1

using excel>data>data analysis>ANOVA

we have

Anova: Two-Factor With Replication
SUMMARY	SQ	PQ	TQ	Total
New York
Count	6	6	6	18
Sum	120	69	144	333
Average	20	11.5	24	18.5
Variance	8	19.9	35.6	47.44118
New Jersey
Count	6	6	6	18
Sum	104	142	131	377
Average	17.33333	23.66667	21.83333	20.94444
Variance	29.86667	35.46667	82.96667	51.11438
Total
Count	12	12	12
Sum	224	211	275
Average	18.66667	17.58333	22.91667
Variance	19.15152	65.53788	55.17424
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	53.77778	1	53.77778	1.52345	0.22668	4.170877
Columns	190.7222	2	95.36111	2.701448	0.083414	3.31583
Interaction	425.7222	2	212.8611	6.03006	0.006292	3.31583
Within	1059	30	35.3
Total	1729.222	35

a) the hypotheses for this experiment is

Ho: there is no interaction between states and benifits of programme

b) given above

c)Yes , because p value of interaction is less than 0.5

d) Make your decision(s): Reject Ho

e) there is no interaction between states and benifits of programme