Emma\'s On-the-Go, a large convenience store that makes a good deal of money fro

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 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: GroupSample sizeSample meanSample varianceFront42213.1400.4Left-hand side42217.0771.0Right-hand side42225.3283.2 Send data to Excel 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.

Give an estimate of this common population variance by pooling the sample variances given:

Give an estimate of this common population variance based on the variance of the sample means given:

Explanation / Answer

Group Sample Size Sample Mean Sample Variance
front 42 213.1 400.4
left hand side 42 217.0 771.0
right hand side 42 225.3 283.2

The estimate of the common population variance by pooling the sample variances is:

² = [(42)(400.4) + (42)(771.0) + (42)(283.2)] / (42 + 42 + 42) = 484.8

(Since the sample sizes are all the same, the same result is obtained by simply averaging the sample variances.)

The other question that is asked with the previous question is "Give an estimate of this common population variance based on the variance of the sample means given."

To calculate this estimate, you first need to find the "grand mean", which is the mean of the sample means:

X(grand mean) = [(42)(213.1) + (42)(217.0) + (42)(225.3)] / (42 + 42 + 42) = 218.467

² = 42[(213.1 - 218.46)² + (217 - 218.46)² + (225.3 - 218.46)²] / 2 = 1630.583

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