Question

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? (Select all that apply.)

a. sample of size n from the population has an equal chance of being selected.
b. Every member of the population has an equal chance of being included in the sample.
c. The simplest method of selection is used to create a representative sample.
d. Each subset of the population has an equal chance of being included in the sample.
e. Every sample of size n from the population has a proportionally weighted chance of being selected.

Answer 1

A simple random sample of measurements from a population is selected such that every member of the population has an equal chance of being included in the sample, each subset of the population has an equal chance of being included, and a sample of size n has an equal chance of being selected.

Step-by-step explanation:

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

1. Every member of the population has an equal chance of being included in the sample. This ensures that the sample is representative of the larger population and reduces sampling bias.
2. Each subset of the population has an equal chance of being included in the sample. This means that any group of individuals within the population has the same probability of being selected.
3. A sample of size n from the population has an equal chance of being selected. This ensures that all possible samples of the same size have an equal probability of being chosen.

Answer 2

a) sample of size n from the population has an equal chance of being selected.

b) Every member of the population has an equal chance of being included in the sample.

Step-by-step explanation:

Simple random sampling:

• It is a type of probabilistic sampling.
• It is an unbiased representation of population.
• The probability of selection is equal for every observation.
• A sample is taken in such a way that each member has an equal probability of being selected.
• A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.
• Thus,the correct interpretation is given by,

a) sample of size n from the population has an equal chance of being selected.

b) Every member of the population has an equal chance of being included in the sample.

• c) The simplest method of selection is used to create a representative sample.

The statement is false.

There is no pattern or technique used for selection. The selection is purely random.

• d) Each subset of the population has an equal chance of being included in the sample.

The statement is false.

Each object of the population has an equal chance of being included in the sample. and not each subset.

• e) Every sample of size n from the population has a proportionally weighted chance of being selected.

The given statement is false.