Question

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

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.