Question

It might be predicted that consumer buying behavior would vary with the location of products in a store. Therefore, a team of market researchers looked at the sales per day for a well-known and unknown brand of candy bars. Additionally, the researchers placed the candy bars in the usual location and next to the cash register in different stores. What can the market researchers conclude with an α of 0.05?

known brand/ usual	known brand/ cash register	unknown brand/ usual	unknown brand/ cash register
16 24 19 17 26 30 18	25 15 16 20 31 27 19	11 6 9 13 14 7 11	19 18 16 21 22 17 19

a) Compute the appropriate test statistic(s) to make a decision about H₀.
Location: critical value =  ; test statistic =  


Brand: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

Interaction: critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0


b) Compute the corresponding effect size(s) and indicate magnitude(s).
Location: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Brand: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect
Interaction: η² =  ;  ---Select--- na trivial effect small effect medium effect large effect


c) Make an interpretation based on the results.

There is a location difference on candy bar sales.There is no location difference on candy bar sales.     

There is a brand difference on candy bar sales.There is no brand difference on candy bar sales.     

There is a location by brand interaction on candy bar sales.There is no location by brand interaction on candy bar sales.

Answer 1

a)

data

	known brand	unknown brand
usual	16	11
	24	6
	19	9
	17	13
	26	14
	30	7
	18	11
cash register	25	19
	15	18
	16	16
	20	21
	31	22
	27	17
	19	19

result

Anova: Two-Factor With Replication
SUMMARY	known brand	unknown brand	Total
usual
Count	7	7	14
Sum	150	71	221
Average	21.42857	10.14286	15.78571
Variance	27.95238	8.809524	51.25824
cash register
Count	7	7	14
Sum	153	132	285
Average	21.85714	18.85714	20.35714
Variance	35.47619	4.47619	20.86264
Total
Count	14	14
Sum	303	203
Average	21.64286	14.5
Variance	29.32418	26.57692
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	146.2857	1	146.2857	7.627561	0.010848	4.259677
Columns	357.1429	1	357.1429	18.62197	0.000237	4.259677
Interaction	120.1429	1	120.1429	6.264432	0.019528	4.259677
Within	460.2857	24	19.17857
Total	1083.857	27

Compute the appropriate test statistic(s) to make a decision about H₀.
Location: critical value = 4.259677 ; test statistic =   146.2857
Decision - reject Ho

Brand: critical value =4.259677    ; test statistic =  

357.1429

Decision:  --Reject H0

Interaction: critical value =4.259677   ; test statistic =  

120.1429

Decision:  -Reject H0