Assume that you work for a chain of food stores and that you are interested

Assume that you work for a chain of food stores and that you are interested
in how your company’s prices compare with your competitors. Since a food store
carries many items, it is likely that you are higher on some products than on others.
The goal of the study is to determine whether or not you can claim to be
“significantly” lower in price than any of your competitors.
A random sample of 36 products, from the thousands available, were priced
at six food stores in the Macomb, Illinois area in 1980. The prices are attached. If a
“name” brand existed for a product, the same “name” brand was priced at all the
eight stores, if possible. In addition, if a store had an equivalent “house” brand, its
price was also recorded. (Note that W. Pierce has no “house” brands.) The data is
contained in the EXCEL file “grocdata.xls” included in the supplementary files for
this Module. You will note, as you look at the data, that some data is missing and
also that in some cases, the “house” brand costs more than the “name” brand
(probably resulting from a sale on the day of the price check).
Assignment:
You are to assume that you are employed at one of the five stores (do not
pick W. Pierce). You are to determine if your store is “significantly” lower or
higher in cost than the other five stores listed. You need to pick a “market basket”
of items by randomly picking 25 of the 36 items on which to base a decision. For
each of the items chosen, you should randomly decide if you will include the “name”
or “house” brand of that item in your “market basket”.
Knowledge of your company’s relative position compared to the other
companies would be quite useful in advertising. If you turn out to be “significantly”
lower you could use this fact in your ads. If you turn out to be the same as the other
companies you might wish to emphasize service, quality, or brand selection in your
advertising. If you turn out to be “significantly” higher, I’m not sure you could
“spin” the result but perhaps such a result would lead to deeper questions about the
management of the company.
You should work with an overall alpha level of .05.

Hints:
After you have chosen your “market basket” you may find you have chosen
one of the products for which the price is missing. You should develop
some rationale for estimating a price for this product as it is undoubtedly
available. Examples of how you might estimate a price include using the
average value of all the stores for which you do have prices (which makes
sense for “name” brands), or if a “house” brand you might find that the
price in your store is always approximately some fixed percentage lower
than the “name” brand price. Also, regression analyis might be helpful.
There are many other possibilities. Be sure to include a discussion of this
issue and include in your report a listing of the actual items and the prices
(either actual or estimated) that you will be analyzing.
It is clear that you cannot analyze the data as it is since you would be in some
cases literally comparing apples to oranges. Some kind of transformation
is necessary before you begin your analysis. One approach might be to
compute the average or median price for each row (e.g. Cabbage) and
replace the price for that item at each store by the percentage above (+)
or below (-) the mean or median price. For example the prices of
“name” brand sugar are $2.09, $1.69, $1.70, $1.64, $2.13, and $1.99 per
five pound bag (remember this is 1980). Since the average price is $1.87,
these would convert to 11.6%, -9.8%, -9.3%, -12.5%, 13.7%, and 6.23%
of the average price. Similar figures could be computed based on the
median. Be sure to include a discussion of this issue in your report as
well as a clear listing of the transformed data you will actually be
analyzing.
3) W. Pierce does not sell “house” brands. Thus, even if you were willing to
buy a non-name brand product at W. Pierce, you couldn’t. Therefore, at W. Peirce,
de facto, the “house” price is identical to the “name” price