Question

The International 500. In Exercise 1.49 on page 16, you used simple random sampling to obtain a sample of 10 firms from Fortune Magazine's list of "The International 500."

(a) Use systematic random sampling to accomplish that same task.

(b) Which method is easier: simple random sampling or systematic random sampling?

(c) Does it seem reasonable to use systematic random sampling to obtain a representative sample? Explain your answer.

Short answer

Part (a)The sample is 37, 87, 137, 187, 237, 287, 337, 387, 437, and 487.

Part (b) Systematic random sampling is easier to simple random sampling.

Part (c) No. systematic random sampling is not reasonable to obtain a representative sample.

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

In Exercise 1.49 on page 16, you used simple random sampling to obtain a sample of 10 firms from Fortune Magazine's list of "The International 500."

Part (a) Step 2. Obtain a sample of size 10 using systematic random sampling.

First, divide the population size by the sample size and then round off the result to the nearest whole number(m).

In this case, the population size is 500.

and the sample size is 10.

$$\begin{gathered} m=\frac{500}{10} \\ =50 \end{gathered}$$

Part (a) Step 3. Obtain a sample of size 10 using systematic random sampling.

Now obtain a number kbetween 1 to mby using MINITAB:

Step 1: Select Calc > Random Data Integer from the MINITAB menu.

Step 2: Enter twice your intended sample size in the Number of rows of data to create a section, just in case there are repeats. Enter 1 as the sample size.

Step 3: In the Store column, type Number in column C1

Step 4: Enter 01 as the minimum value.

Step 5: Enter 50 as the maximum value.

Step 6: Select OK.

OUTPUT FROM MINITAB:

NUMBER $k=37$

Part (a) Step 4. Obtain a sample of size 10 using systematic random sampling.

Now select the numbers k, k + m,...., k + 4m to generate the sample.

$$\begin{gathered} k=37 \\ k+m=37+50 \\ =87 \\ k+2m=37+2\left(50\right) \\ =137 \\ k+3m=37+3\left(50\right) \\ =187 \\ k+4m=37+4\left(50\right) \\ =237 \\ k+5m=37+5\left(50\right) \\ =287 \\ k+6m=37+6\left(50\right) \\ =337 \\ k+7m=37+7\left(50\right) \\ =387 \\ k+8m=37+8\left(50\right) \\ =437 \\ k+9m=37+9\left(50\right) \\ =487 \end{gathered}$$

The sample is 37, 87, 137, 187, 237, 287, 337, 387, 437, and 487.

Part (b) Step 1. Identify if simple random sampling is easier or systematic random sampling.

Systematic random sampling is much easier to conduct if we compare it with simple random sampling.

The reason being there are some disadvantages to simple random sampling. That is, in some cases, it does not provide enough information about the subpopulations.

Furthermore, when the population members are dispersed, making this method of sample collection is impractical.

Part (c) Step 1. Identify if using systematic random sampling to obtain a representative sample is reasonable or not.

If the sample is not linked to the size of sales that are not in the United States, systematic sampling would apply.

However, in this case, the ranking is based on sales.

When the value of $k=2$is low, the sample will comprise enterprises with higher sales outside of the United States than the population as a whole.

When the value of $k=49$is high, the sample would, on average, contain firms with lower sales than the population as a whole.

In both circumstances, the sample would not be typical of the population in terms of sales outside the United States.