Chapter 4: Q 26. (page 228)

Systematic random sample Sample surveys often use a systematic random sample to choose a sample of apartments in a large building or housing units in a block at the last stage of a multistage sample. Here is a description of how to choose a systematic random sample. Suppose that we must choose $4$ addresses out of $100$ Because $100 / 4 = 25$ we can think of the list as four lists of $25$ addresses. Choose $1$ of the first $25$ addresses at random using Table D. The sample contains this address and the addresses $25, 50,$ and $75$ places down the list from it. If the table gives $13,$ for example, then the systematic random sample consists of the addresses numbered $13, 38, 63,$ and $88$
(a) Use Table D to choose a systematic random sample of $5$ addresses from a list of $200$ Enter the table at line $120$
(b) Like an SRS, a systematic random sample gives all individuals the same chance to be chosen. Explain why this is true. Then explain carefully why a systematic sample is not an SRS.

Short Answer

Expert verified

Part (a) The selected addresses are $35, 75, 115, 155,$ and $195$

Part (b) Because there is no chance of selecting the first five individuals for the sample.

Step by step solution

Part (a) Step 1: Given information

At the end of a multistage sample, a systematic random sample is frequently used to select a sample of apartments in a large structure or housing units in a block.

Part (a) Step 2: Concept

A simple random sample (SRS) of size $n$ is made up of $n$ people chosen from the population with an equal chance of being the sample that is actually chosen.

Part (a) Step 3: Explanation

Line $120$ of table D is as follows:

$35435, 43742, 11937, 35476, 55972, 39421, 65850, 04266, 35435, 43742,$

Divide the $200$ addresses into five groups of $40$ The numbers are $35, 75, 115, 155,$ and $195,$ and we're seeking for $2 -$ digit numbers.

Part (b) Step 1: Explanation

We know that each address has an equal probability of getting chosen, which is $1$ in $40$ That does not imply that each subset has an equal chance of getting chosen. As a result, it is not an SRS because picking the first five individuals for the sample is impossible.