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The population comprises all students of the statistics class. It is required to obtain a sample of size six.

a.

In a simple random sampling, the subjects are chosen from the population in such a way that no particular pattern is followed, and the probability of being selected in the sample is the same for any student.

The aim is to form a simple random sample containing six students from the statistics class. The below steps are followed:

1. Make identical-looking chits using the roll numbers of students and shuffle them in a bowl.

2. Pick six chits from the bowl.

Thus, the six students have an equal chance of being selected.

b.

In systematic sampling, the subjects are chosen from the population in such a way that a certain pattern is followed for choosing each subject after the first one is randomlychosen from the population.

The aim is to form a systematic sample containing six students from the statistics class. The below steps are followed:

1. Align all students in a straight line randomly.

2. Select any student at random from the class.

3. After selecting the first student at random, select every 10^th(k) student in the line until six students are selected.

Note: K can be any random number that stays constant throughout the sampling.

Thus, the six students are selected by systematic sampling.

c.

In stratified sampling, random samples are taken from each of the strata. The strata are designed in such a way that they share a common characteristic.

The aim is to form a stratified sample containing six students from the statistics class.

The below steps are followed:

1. Divide the students into two groups, say based on gender(strata).

2. Select three students from each of the groups.

Thus, the six students are selected as stratified sampling.

d.

In cluster sampling, each of the items from randomly selected clusters is surveyed for a response. The clusters are identical.

The aim is to form a cluster sample containing six students from the statistics class. The below steps are followed:

1. As per the random seating arrangement of students in the class, divide the students in a row-wise manner in a set of three.

2. Select any two rows randomly.

3. Collect responses from all the students of the two rows.

Thus, the six students are selected as cluster sampling.