Question

1. A statistics student takes a poll five randomly selected coffee shops, then randomly selects 6 customers from each coffee shop to find out if they support the President’s decision for declaring the construction of a southern border wall a national emergency.

Why wouldnʹt this sample be representative of the entire US voting population?

Answer 1

Following are reasons :

1. Sample would consist of only those voters who happen to visit those five randomly selected coffee shops. All those voters who were not at the coffee shops at the time of sampling will not be included in the sample. Hence, the sample will not be sufficiently representative of full voting population.

2. Within the set of selected 5 coffee shops, the student only collects survey of randomly selected 6 customers. So this may not be a large enough sample to represent the overall opinion of even a single coffee shop.

3. Those voters who do not visit coffee shops at all i.e. those who never drink coffee have zero probability of being included in the sample. So the collected sample will miss out on gathering opinion of such people.  

4. If the randomly selected coffee shops happen to be geographically located near the southern region of US. then it is likely that such a sample will be heavily biased towards one particular opinion as opposed to the voters living in other parts of the country. As a result, the sample would reflect a very biased picture.

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