# Sampling and statistical inference – report and excel spreadsheet

Beltway Shoe Company sells luxury leather shoes in the United States. The company monitors its shoe sales by collecting randomly chosen data from store locations throughout the country. They record original price, sale price, and number of days it takes to sell each unit. Each pair of shoes is classified as “Eastern Region” if it is sold in the Eastern part of the United States, or as “Western Region” if it is sold in the Western part of the country. Randomly chosen samples provided sales data for 50 Western Region and 50 Eastern Region pairs of shoes. The complete data set is in the file named Shoes, attached in Excel document

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Managerial Report
Prepare a report (see below) that summarizes your assessment of the nature of the shoe market in each region. Be sure to include the following seven (7) items in your report.

1. Descriptive statistics (mean, median, range, and standard deviation) to summarize each of the three variables for the 50 Western Region shoes. Are there any outliers in the data set for any of the three variables? If there are any outliers in any category, please list them and state for which category they are an outlier. Describe which method you used to make your determination.
2. Descriptive statistics (mean, median, range, and standard deviation) to summarize each of the three variables for the 50 Eastern Region shoes. Are there any outliers in the data set for any of the three variables? If there are any outliers in any category, please list them and state for which category they are an outlier. Describe which method you used to make your determination.
3. Compare your summary results from #1 and #2. Discuss any specific statistical results that would help the Beltway Shoes Marketing Department understand the regional shoe market.
4. Develop a 90% confidence interval estimate of the population mean sales price and population mean number of days to sell for pairs of Beltway Shoes in the Eastern Region. Interpret your results.
5. Develop a 90% confidence interval estimate of the population mean sales price and population mean number of days to sell for pairs of Beltway Shoes in the Western Region. Interpret your results.
6. Assume a branch sales manager requested estimates of the mean selling price of Western Region shoes with a margin of error of \$5 and the mean selling price of Eastern Region shoes with a margin of error of \$4. Using 90% confidence, how large should the sample sizes be for each?
7. A Western Region store manager just placed on display a pair of Beltway Shoes, with an original price of \$120.  Also, an Eastern Region store manager just placed on display a pair of Beltway Shoes, with an original price of \$125. For each pair of shoes, what is your estimate of the final selling price (based on the percent difference for the sale and list price) and number of days required to sell each of these units?

Write a report, you should have in-text citations and a reference page.

Your report must contain following:

• A title page in APA style.
• An introduction that summarizes the problem.
• The body of the paper should answer the questions posed in the problem by communicating the results of your analysis. Include results of calculations, as well as charts and graphs, where appropriate.
• A conclusion paragraph that addresses your findings and what you have determined from the data and your analysis.

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