Question

A group of physicians were interested in understanding more about how much exercise their patients get each week. They randomly selected patients from their practice and asked each patient how much they exercise each week, in hours. With 95% confidence, they estimated that their patients exercise on average 3.1 hours per week with a margin of error of 1.4.

Why do you thin it was important for the physicians to randomly select patients to include in their sample? How would this be different if they took a convenience sample?

Answer 1

A random sample was necessary to obtain since that will ensure that the selected sample is unbiased and follows a parent population distribution(normal distribution or student's t distribution).

It is necessary for the population from which the sample is selected, to follow some standard distribution so as to calculate the critical values for the computation of confidence intervals.

Had the sample been conveniently collected, it would be biased and would not represent the true nature of the population.

For example, let patients of all age groups visit the physicians. However, on the day that the (convenience)sample was surveyed, only children have appointments. In such a situation, the sample will only comprise of children and will be biased since the actual group of patients who visit the physicians are from all age groups. So, the children-sample would not be true representative of the parent population.

Hence, the collected sample must be random.