6) A small business owner you follow on TikTok is SO EXCITED because last month, she was able to begin selling her product in a popular chain store around the nation. Her contract with the chain store says that at any time, there will be at least 20 of her products sitting out on the shelves. She wants to conduct a survey to see if that is true. She visits 5 of the local chain stores around her and records the number of products of hers that are on the shelves. She will then construct a 95% confidence interval to determine the mean number of products on the shelves for all of the stores. (a) Discuss whether this study meets the each of the conditions for constructing a confidence interval. If one of the conditions has not been met, what additional information would be required or what change in the study would you recommend?

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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6) A small business owner you follow on TikTok is SO EXCITED because last month, she was able to begin
selling her product in a popular chain store around the nation. Her contract with the chain store says that at any
time, there will be at least 20 of her products sitting out on the shelves. She wants to conduct a survey to see if
that is true. She visits 5 of the local chain stores around her and records the number of products of hers that are
on the shelves. She will then construct a 95% confidence interval to determine the mean number of products on
the shelves for all of the stores.
(a) Discuss whether this study meets the each of the conditions for constructing a confidence interval. If one of
the conditions has not been met, what additional information would be required or what change in the study
would you recommend?
(b) If, instead of constructing a 95% confidence interval, the business owner constructed a 98% confidence
interval, would the 98% interval be wider, narrower, or the same width as the 95% interval? Explain.
(c) How would the width of confidence interval change if she took a larger sample? Explain.
Transcribed Image Text:6) A small business owner you follow on TikTok is SO EXCITED because last month, she was able to begin selling her product in a popular chain store around the nation. Her contract with the chain store says that at any time, there will be at least 20 of her products sitting out on the shelves. She wants to conduct a survey to see if that is true. She visits 5 of the local chain stores around her and records the number of products of hers that are on the shelves. She will then construct a 95% confidence interval to determine the mean number of products on the shelves for all of the stores. (a) Discuss whether this study meets the each of the conditions for constructing a confidence interval. If one of the conditions has not been met, what additional information would be required or what change in the study would you recommend? (b) If, instead of constructing a 95% confidence interval, the business owner constructed a 98% confidence interval, would the 98% interval be wider, narrower, or the same width as the 95% interval? Explain. (c) How would the width of confidence interval change if she took a larger sample? Explain.
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