Q 21. - Elementary Statistics

Question

Top North American Athletes. Refer to Problem 17. 

(a)  Use systematic random sampling to obtain a sample of 15 athletes.

(b) In this case, is systematic random sampling an appropriate alternative to simple random sampling? Explain your answer.

Step-by-Step Solution

Answer

Part (a) 002, 009, 016, 023, 030, 037, 055, 051, 058, 065, 072, 079, 086, 093, 100.

Part (b) Yes. 

Part (a) Step 1. Given information.

The given statement is:

Problem 17 says that the best 100 North American athletes of the twentieth century were ranked by an ESPN panel.

We have to select a sample using systematic random sampling.

Part (a) Step 2. Obtain a sample of 15 athletes by using systematic random sampling.

A total of 100 North American athletes were ranked.

Therefore, the given population is 100.

$N=100$

Our sample size is: 15

$n=15$

Therefore, the proportionality is:

$$\begin{gathered} \frac{N}{n}=\frac{100}{15} \\ =6.67 \end{gathered}$$

Its nearest whole number is 7.

Therefore, $m=7$.

Part (a) Step 3. Obtain a sample of 15 athletes by using systematic random sampling.

Now use the random numbers table to obtain a number, between k and 7:

So, $k=2$.

After it, select those samples that are numbered $k, k+m, k+2m, ...$

The samples of 15 athletes are:

002, 009, 016, 023, 030, 037, 055, 051, 058, 065, 072, 079, 086, 093, 100.

Part (b) Step 1. Identify if systematic random sampling is an appropriate alternative to simple random sampling in this case.

Yes. 

Here systematic random sampling is a better option than simple random sampling. Because every sample has an equal chance of getting selected.