Suppose that we are interested in the population of all undergraduate students a

Question

Suppose that we are interested in the population of all undergraduate students attending the University of Boston. We want to look at the GPAs of these students and calculate the average GPA for University of Boston undergraduates. If we wanted to make inferences about this population information using a sample, explain what a representative sample would be and how we might obtain one. In your explanation, also provide at least two examples of samples that would not be representative and explain why they are not representative.

Explanation / Answer

If we randonly select 10 students from each department/course of the university and then use this to calculate the average, we will get a representative sample of the population. Each department/course will have considerable variation in grades and hence this sampling technique will ensure that all groups are represented (stratified sampling technique)

Non representative sample 1 - Chosing any 5 courses under the universtity and then using the grades of all students attending these courses. This method of sampling is cluster sampling. Here, all courses are not represented.

Non representative sample 2 - Standing near the cafeteria of university and randomly surveying students. Here also, we are not guaranteed to get a representative sample based on the location of the cafeteria or based on the timings of different departments.

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