Answer:
Explained below.
Step-by-step explanation:
In this case we need to select a sample of 6 students from the entire statistics class.
(a)
A simple random sample is a part of a statistical population in which every individual of the population has an equal probability of being selected.
Assigning each individual of the population a unique number and using a computer or random number generator for selection is a procedure to select a simple random sample.
So, we can assign unique numbers to each student in the class and use a random number generator to select any six.
(b)
Systematic sampling is a kind of probability sampling method in which individuals from a larger population are nominated according to a random initial point and a static, periodic interval.
For instance, consider a study where the researcher first selects a name randomly from the alphabetized order and then follow a fixed pattern of selecting every 10th person from the population.
Suppose there are <em>n</em> students in the class.
And the first student selected is the <em>k</em>th student. Then the remaining five can be selected in a equal interval of <em>k</em> students.
That is, the second student selected will be the 2kth student, the 3rd will be the 3kth, the 4th will be the 4kth, the 5th will be the 5kth and the 6th will be the 6kth.
The sample selected will be a systematic random sample.
(c)
Stratified sampling is a kind of sampling in which whole population is distributed into homogeneous subgroups before one takes a sample. These subgroups are called strata which is mutually exclusive or related.
In this process the population members cannot be excluded.
To select six students we first divide the entire class into 6 subgroups or 6 strata.
Then select one student from each group.
The sample selected will be a stratified random sample.
(d)
Cluster Sampling is a method to randomly select samples from a population that is too enormous for simple random sampling.
Using cluster sampling, the experimenter distributes the entire population into distinct groups, called clusters.
Then, a simple random sample of clusters is chosen from the population. Then the experimenter performs the analysis on data from the sampled clusters.
To select a cluster sample, first divided the entire class into various small groups consisting of 2 or 3 students each.
Then select a simple random sample of these groups to select 6 students.
The sample selected will be a cluster sample.
