Confidence interval for population mean:

Susan Thurston, product manager for Consolidated Foods Inc., is responsible for developing and evaluating promotional campaigns to increase sales for her canned food product. She has just been appointed product manager for Brand 1, which competes in retail food markets with four other major brands. The product is well established in a stable market and is generally viewed by consumers as a food commodity. Successful product performance requires strategies that encourage customers to move to Susan's brand from the various competing brands. She can encourage this movement by various combinations of reduced price specials, in-store displays, and newspaper advertising (partial support for a weekly supermarket ad that emphasizes Brand 1). Her competitors have at their disposal the same strategic tools for increasing their sales. By successfully manipulating these marketing variables relative to the actions of her competitors, Susan works to develop a successful sales performance record, as demonstrated by a stable or increasing market share.

Susan believes that her future success depends on her knowledge of the market.  Therefore, she has asked for your help in analyzing the past year of weekly data. Your task is to provide Susan with information and a solid understanding of the market. You will compare the sales performance of Brand 1 with that of its market competitors. Then you will develop your analysis and provide a carefully written description of the conclusions you have drawn from your work. From your report, Susan will gain an understanding of the market so that she can develop optimal marketing strategies.

Supermarket sales data for analysis and evaluation are routinely purchased from a national marketing research company. Your analysis will use data from three major supermarket chains that together distribute 60 percent of the product. The marketing research department has obtained weekly brand tracking data for the three chains for the past year.  The variable list is shown in the table at the end, and the data are stored in an Excel file named Confood. These data include weekly sales, price, and promotion data for Susan's product and its four major competitors. It is collected from weekly sales audits in specific supermarkets, whose sales patterns follow national trends.  Data from supermarkets in the same distribution chain are aggregated.

Comparing Sales for Competing Brands:

A report on last year's sales performance is being prepared, and you have been asked to assist with the statistical analysis.  Nina Gupta, Confood's vice president of marketing, has asked for a report on the sales status of Brand 1 in comparison with the four competing brands.  This report will be used to determine product sales performance relative to the rest of the market.  She has asked for an estimate of average weekly sales (number of units sold), average weekly price, market share (percentage of units sold by each brand), and average weekly sales revenue.  In addition, she has asked for a comparison of brand 1 and Brands 2 and 4 with respect to these measures.

After discussion with Susan you conclude that a combination of classical estimation and hypothesis testing will provide the desired statistical results for your study.  Therefore, you agree that you will first prepare 95 percent confidence intervals for the four measures requested by Ms. Gupta.

In the past, Brand 2 has been the leading seller, and Brand 1 has usually been ahead of Brand 4 in total sales and revenue.  You decide to perform a test to determine whether Brand 2 is still ahead of Brand 1 in average weekly sales and average weekly revenue.  A second test will be used to determine whether Brand 1 remains ahead of Brand 4 on these measures.  You agree to design and implement appropriate hypothesis tests to answer these questions.  After the Confood data file has been loaded into Excel, the above mentioned analysis will involve the following tasks.

Write a one-page report to Ms. Gupta presenting your conclusions regarding the market performance of Brand 1.  This report should clearly indicate the sales performance for Brand 1 and should compare it to the performance of the competition.  In an appendix, you many include tables and graphs to show the results of your analysis and help communicate your conclusions.