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.

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.

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, $m=7$.

Now use the random numbers table to obtain a number, between kand 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.

Yes.

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