Chapter 7, Problem 42SE

Shadow Stocks. Jack Lawler, a financial analyst, wants to prepare an article on the Shadow Stock portfolio developed by the American Association of Individual Investors (AAII). A list of the 30 companies in the Shadow Stock portfolio is contained in the file ShadowStocks. Jack would like to select a simple random sample of 5 of these companies for an interview concerning management practices.

1. a. In the file ShadowStock, companies are listed in column A of an Excel worksheet. In column B we have generated a random number for each of the companies. Use these random numbers to select a simple random sample of 5 of these companies for Jack.
2. b. Generate a new set of random numbers and use them to select a new simple random sample. Did you select the same companies?

To determine

Select a simple random sample of 5 of the given companies using the given random numbers.

Answer to Problem 42SE

The random sample of 5 of the given companies is tabulated below:

Company	Random Number
LMI Aerospace	0.008012
Alpha & Omega Semiconductor	0.055369
Olympic Steel	0.059279
Kimball International	0.144127
International Shipholding	0.227759

Explanation of Solution

Calculation:

The given data represent the Shadow Stock of 30 companies.

Step-by-step procedure to obtain a simple random sample.

• Open the data file Shadow Stocks.
• Sort the random numbers and the corresponding company names into an ascending order.
• Select the companies associated with the first five smallest random numbers.

Thus, the random sample of 5 of the given companies is tabulated below:

Company	Random Number
LMI Aerospace	0.008012
Alpha & Omega Semiconductor	0.055369
Olympic Steel	0.059279
Kimball International	0.144127
International Shipholding	0.227759

To determine

Generate a new random set of random numbers and select a new simple random sample.

Check whether the companies in the new simple random sample are the same as in Part (a).

Answer to Problem 42SE

The new simple random sample of the given companies is as follows:

Company	Random Number
Five Star Quality Care	0.018590
SigmaTron International	0.085862
CSS Industries	0.097172
REX American Resources Corp	0.122113
VOXX International Corp	0.158389

The companies in the new random samples do not match with the companies in the random sample of Part (a).

Explanation of Solution

Calculation:

A new simple random sample is to be obtained.

Software procedure:

Step-by-step software procedure to obtain a random sample using EXCEL.

• Open the EXCEL.
• Enter company names in column A.
• Generate a new set of random numbers using the formula “=RAND()” in column B.
• Sort the random numbers and the corresponding company names into an ascending order.
• Select the companies associated with the first five smallest random numbers.

The output obtained using EXCEL software is as follows:

Therefore, the random sample of 5 of the given companies is as follows:

Company	Random Number
Five Star Quality Care	0.018590
SigmaTron International	0.085862
CSS Industries	0.097172
REX American Resources Corp	0.122113
VOXX International Corp	0.158389

Here, it is observed that the companies in the new random sample do not match with the companies in the random sample of Part (a).