Address the following prompts about random samples: (1-a) give a concrete exampl

Question

Address the following prompts about random samples:

(1-a) give a concrete example of a research question in which you obtained a truly random sample.

(1-b) Explain why, in this case, your sample could be considered “truly random.”

(2-a) give a concrete example of a research question in which you did NOT obtain a truly random sample, yet your conclusion based on that sample would be meaningful and not misleading.

(2-b) Explain why, in this case, your conclusion would be meaningful.

(3-a) give a concrete example of a research question in which you did NOT obtain a truly random sample, and this would cause your conclusion based on these results to be misleading or meaningless.

(3-b) Explain why, in this case, your conclusion would not be meaningful.

It seems the "truly random sample" here means unbiased, and my main question is how to say the case is meaningful? Could you give me few examples and explain them with detailed logical analysis?

Explanation / Answer

(1-a) Suppose we want to study the performance of students in a class through their average final score.and thus we randomly select a sample of students from the class.

(1-b) This is considered as truly random sample as ww randomly select the students from the class without giving preference to any student.

(2-a) Suppose we want to study the performance of school students in a country through their average final score.and thus we randomly select a sample of students from few schools of the country instead of all the school of the country and we can draw meaningful conclusion from it.

(2-b) The conclusion from such sample would be meaningful if the sample is drawn from those school which can significantly capture the variability in the data for all the school of the country.

(3-a) Suppose we again want to study the performance of school students in a country through their average final score and thus we randomly select a sample of students from few schools of the country instead of all the school of the country .

But we select the sample from those schools only which are known to produce good acdemics results thus ignoring the schools where the performance of the students might not be as good as compared to other schools.

(3-b) The conclusion from such sample would not be meaningful as the sample obtained in a manner which do not capture the complete variability of the data and would thus produce misleading results.

Hence we say that the sample is considered "truly random sample" if it can produce the unbiased results, such as in the first case.

(2-a) Suppose we

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