Emma's Ön-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 50 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: Sample Sample size Sample variance Group mean Front 50 223.6 428.4 Left-hand side 50 220.5 246.4 Right-hand side 50 213.8 512.5 Send data to calculator 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 thre one decimal place. decimal places and rounding your responses to at least (a) Give an estimate of this common population variance by pooling the sample variances given. (b) Give an estimate of this common population variance based on the variance of the sample means given.

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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 50 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
size
mean
variance
Front
50
223.6
428.4
Left-hand side
50
220.5
246.4
Right-hand
side
213.8
512.5
Send data to calculator
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.
(a) Give an estimate of this common population variance by
pooling the sample variances given.
(b) Give an estimate of this common population variance based
on the variance of the sample means given.
50
Transcribed Image Text: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 50 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 size mean variance Front 50 223.6 428.4 Left-hand side 50 220.5 246.4 Right-hand side 213.8 512.5 Send data to calculator 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. (a) Give an estimate of this common population variance by pooling the sample variances given. (b) Give an estimate of this common population variance based on the variance of the sample means given. 50
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