A simple random sample of n measurements from

ka073104

ka073104

Answered question

2022-04-11

A simple random sample of n measurements from a population is a subset of the population selected in a manner such that which of the following is/are true?

Answer & Explanation

Vasquez

Vasquez

Expert2023-04-27Added 669 answers

A simple random sample of n measurements from a population is a subset of the population selected in a manner such that:
1. Each member of the population has an equal chance of being selected for the sample.
2. The selection of one member of the population is independent of the selection of any other member.
These two conditions ensure that the sample is representative of the population and that the statistical analysis of the sample can be extended to the population as a whole.
To illustrate, let's consider a population of size N and a simple random sample of size n. The number of possible samples of size n that can be selected from the population is given by the combination formula:
(Nn)=N!n!(Nn)!
Each of these possible samples is equally likely to be selected if the sample is selected in a simple random manner.
For example, if we have a population of 10 people and we want to select a simple random sample of size 3, there are:
(103)=10!3!7!=120
possible samples that can be selected. Each of these 120 possible samples has an equal chance of being selected if we select the sample in a simple random manner.
In practice, simple random sampling can be achieved using various techniques such as lottery method, random number generators, etc.

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