Question

Keno. In the game of keno, 20 balls are selected at random from 80 balls numbered 1-80. In Exercise 1.48 on page 16, you used simple random sampling to simulate one game of keno.

(a) Use systematic random sampling to obtain a sample of 20 of the 80 balls.

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

(c) Does it seem reasonable to use systematic random sampling to simulate one game of keno? Explain your answer.

Short answer

Part (a) 2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78.

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

Part (c) Yes. It is reasonable to use systematic random sampling to simulate one game of keno.

Step-by-step solution

Part (a) Step 1. Given information. 

The given statement is:

In the game of keno, 20 balls are selected at random from 80 balls numbered 1-80. In Exercise 1.48 on page 16, you used simple random sampling to simulate one game of keno.

Part (a) Step 2. Obtain a sample of size 20 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 80.

and the sample size is 20.

$$\begin{gathered} m=\frac{80}{20} \\ =4 \end{gathered}$$

Now obtain a number kbetween 1 to 4,by using the random number table we obtained the number k as 2.

In the last step, we need to write every 4th number from the list. It will start from 2 and follow the same procedure until we get our 20samples.

Then the resulted numbers will be:

2, 6, 10, 14, 18, 22, 26, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78.

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.

Systematic random sampling usually avoids cases of biasedness, that's why it is reasonable to use systematic random sampling.