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 Sample Sample mean variance Front 2149 276,7 Leht hand side 2056 2733 Right hand side 44 207.0 Assume that the populations of daily sales from which the above samples were drawn are approximately normally distributed and that each has the same mean and the same variance. Answer the following, carrying your intermediate computations to at least three decimal places and rounding your responses to at least one decimal place. TA Give an estimate of this common population variance by pooling Give an estimate of this common population variance based on the Х 5

Answer 1

Group	ni	x̅i	nx̅i	ni*(Xi-Xgrand)2	SS=(ni-1)*s2
1	44	214.9	9455.60	1446.3289	11898.1000
2	44	205.6	9046.40	559.7289	11751.9000
3	44	207	9108.00	206.5556	17346.2000
total=	132		27610.00	2212.6133	40996.2000
	Grand mean=Σnx̅i/Σni=	209.167		SSTr	SSE

df(between)=groups(k)-1=		2
df(error)=N-k=	132-3=	129

MS(b/w) =SS(factor)/df(factor)=		1106.3067
MS(within)=SS(error)/df(error)=		317.8000

Common population variance by pooling sample variance =1106.3

Common population variance by pooling variance of sample mean =317.8