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 Use the Table of Random Digits below to solve.

The owner of a large shopping center wants to survey a sample of 12 store owners and ask them if they would stay open one hour late one evening for a charity event. He divides the stores into two main categories and labels them as shown.

Clothing and Jewelry: 001–150

Food and Services: 151–200

(1)   Suppose the owner wants an equal number of stores from each category. Find the numbers for the stores in the sample if the owner starts at line 108.

(2)   Suppose the owner wants the number of stores in the sample to be proportional to the number of stores in each category. Find the numbers for the stores in the sample if the owner starts at line 116.

 Dec 11, 2019
 #1
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As you can see from the underlined table (red for part (1) and blue for part (2)) , the numbers you want, 6 from each category for the first part, are:

 

Clothing and Jewlery: 011, 106, 135, 138, 109, 071

Food and Services: 157, 163, 154, 197, 174, 185

 

In the second part, your sample should have \(\frac{1}{4} \times 12 =3\) stores from Food and Services category since one fourth of the population is in that category; the rest, 9 stores, should be in the other category. These are underlined in blue:

 

Clothing and Jewlery:070, 143, 043, 036, 024, 117, 092, 126, 136

Food and Services:192, 193, 177

It is very easy to make mistakes reading the random digits table, so you should double check my answers. All you do is start at the line suggested and look at three digits at a time from left to right and select the ones that are in the range of IDs assigned to the stores. Read the table as if the digits followed one another in a continuous stream with no gaps for columns and no breaks for lines because in reality that is how it is and the digits are arranged in columns to give your eyes reference points.

 Dec 11, 2019

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