Question

Emma's On-the-Go, a large convenience store that makes a good deal of money from magazine sales, has three possible locations in the store for its magazine rack: in the front of the store (to attract "impulse buying" by all customers), on the left-hand side of the store (to attract teenagers who are on that side of the store looking at the candy and soda), and in the back of the store (to attract the adults searching through the alcohol cases). The manager at Emma's experiments over the course of several months by rotating the magazine rack among the three locations, choosing a sample of 44 days at each location. Each day, the manager records the amount of money brought in from the sale of magazines. Below are the sample mean daily sales in dollars) for each of the locations, as well as the sample variances: Group Sample size Sample mean Sample variance 44 Front Left-hand side Right-hand side 216.5 211.7 218.3 315.4 450.8 44 44 581.0 Send data to Excel Suppose that we were to perform a one-way, independent-samples ANOVA test to decide if there is a significant difference in the mean daily sales among the three locations. Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place. What is the value of the "between groups" mean square that would be reported in the ANOVA test? 8 What is the value of the "within groups" mean square that would be reported in the ANOVA test?

Answer 1

Treatment	n	X bar	S		n*(X bar - Overall X bar)^2	(n-1)*S^2
Aerobic training	44	216.5	17.7595		44	13562.19313
Resistance training	44	211.7	21.2321		635.36	19384.48903
Aerobic plus resistance training	44	218.3	24.1039		344.96	24982.91379
Total	132			Total	1024.32	57929.59595
k	3
Overall X bar	215.5
	SS	df	MS	F	Significance F
Between Groups	1024.32	2	512.16	1.140499	0.322861138
Within Groups	57929.59595	129	449.0666
Total	58953.91595	131
	SS	df	MS	F
Between Groups	SUM(n*(X bar - Overall X bar)^2)	k-1	SSG/dfG	MSG/MSE
Within Groups	SUM((n-1)*S^2)	n-k	SSE/dfE
Total	SSG+SSE	n-1

MS between = 512.2

MS Within = 449.1