Chapter 5.3, Problem 5.67E

(a)

To determine

To choose a systematic random sample of five from a list of $500$ addresses using table B.

Answer to Problem 5.67E

  $\begin{array}{l}\text{Thus the systematic random sample contains the addresses}\\ \text{numbered 69,169,269,369,469}\text{.}\end{array}$

Explanation of Solution

  $\begin{array}{l}\text{We will first randomly choose an integer between 1 and 100}\text{.}\\ \text{Select the first 2-digit number in the line 130 of table B}\text{.}\\ \text{If the number is between 01 and 99(including), then this integer is selected}\text{.}\\ \text{If the number is 00, then we select the integer 100}\text{.}\\ \text{69}\\ \text{The sample then contains the address numbered 69 and the addresses numbered}\\ \text{100,200,300 and 400 positions above 69}\text{.}\\ \text{69}\\ \text{69+100=169}\\ \text{69+200=269}\\ \text{69+300=369}\\ \text{69+400=469}\\ \text{Thus the systematic random sample contains the addresses}\\ \text{numbered 69,169,269,369,469}\text{.}\end{array}$

(b)

To determine

To find out what is the chance that any specific address will be chosen and explain.

Answer to Problem 5.67E

  $\frac{1}{100}$

Explanation of Solution

  $\begin{array}{l}\text{We randomly chose an integer between 1 and 100}\text{. Thus we have 1 chance}\\ \text{in 100 to select the first address:}\\ \frac{1}{100}\\ \text{Since the other four selected addresses can only be obtained if the(uniquely)}\\ \text{corresponding integer between and 100 is selected, the probability of selecting}\\ \text{any of the other integers is the same as the probability of selecting the}\\ \text{corresponding integer between 1 and 100}\text{.}\\ \frac{1}{100}\end{array}$

(c)

To determine

To explain that why this sample is not a SRS.

Explanation of Solution

A simple random sample SRS selects the sample such that each possible sample has an equal chance to be selected.

The systematic random sample is not a simple random sample because there are samples that cannot be selected while there are samples such as $69,169,269,369,469$ that can be selected and thus all samples are not equally likely to be selected.