cafashions

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Marketing

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Feb 20, 2024

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07-14-2016 CA FASHIONS Cherilyn “Cher” Horowitz is Chief Marketing Officer for CA Fashions, a Los Angeles-based fashion retailer catering to young women with over 350 mall-based stores across the United States. Cher is currently evaluating an in-store kiosk that allows patrons to try on garments virtually, using computer vision and artificial intelligence to automatically determine whether the outfit is a “match” or “mis-match.” Skeptical, Cher has decided to pilot the kiosk in several stores to measure its impact. She will randomly select stores for the pilot, install a kiosk in each one, and monitor the pilot stores’ sales performances for one month. The observed impact of the kiosk will obviously be random for each store. She thinks it is reasonable to assume that the increase in each store’s sales will approximately follow a normal distribution. a) Assume the kiosk has a mean monthly impact of $5,000 with a standard deviation of $2,000. What is the probability that one pilot store chosen at random shows an impact less than $4,000? b) Still assuming that the kiosk has a mean impact of $5,000 and a standard deviation of $2,000, suppose Cher pilots the kiosk at 4 stores. What is the probability that the average impact at the 4 stores is less than $4,000? c) Suppose instead that Cher pilots the kiosk at 16 stores. What is the probability that the average impact at the 16 stores is less than $4,000? d) Now suppose that Cher pilots the kiosk at 64 stores. What is the probability that the © 2016 by the Kenan-Flagler Business School, University of North Carolina, Chapel Hill, NC 27599-3490. Not to be reproduced without permission. All rights reserved. This case was prepared by slaves to fashion (as if) Wendell Gilland, Adam J. Mersereau, Alan W. Neebe as a basis for class discussion rather than to illustrate the effective or ineffective handling of an administrative situation.
2 average impact at the 64 stores is less than $4,000? 1996 by the Kenan-Flagler Business School, University of North Carolina, Chapel Hill, NC 27599-3490. Not to be reproduced without permission. All rights reserved.
3 Cher randomly selected 20 stores for the kiosk pilot. At the end of the month, she month-over- month changes in sales for each of the 20 stores into Excel. The output is as follows: OLD STD IMPACT 1.265 0.3125 5625 1.194 -0.575 3850 1.083 -1.9625 1075 1.308 0.85 6700 1.252 0.15 5300 1.167 -0.9125 3175 1.217 -0.2875 4425 1.263 0.2875 5575 1.279 0.4875 5975 1.303 0.7875 6575 1.143 -1.2125 2575 1.154 -1.075 2850 1.247 0.0875 5175 1.321 1.0125 7025 1.261 0.2625 5525 1.216 -0.3 4400 1.377 1.7125 8425 1.413 2.1625 9325 1.211 -0.3625 4275 1.366 1.575 8150 e) Assume Cher is willing to accept that the true standard deviation of kiosk impact is $2,000. Develop a 95 percent confidence interval for the average impact across all stores. f) Still assuming Cher is willing to accept that the true standard deviation of kiosk impact is $2,000, suppose she wishes her 95 percent confidence interval to be of the form "plus or minus $500". How large a sample should she take to achieve this? g) Assume Cher is no longer willing to accept that the true standard deviation of kiosk impact is $2,000. Develop a 95 percent confidence interval for the average impact across all stores. 1996 by the Kenan-Flagler Business School, University of North Carolina, Chapel Hill, NC 27599-3490. Not to be reproduced without permission. All rights reserved.
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