Answer to Question #38746 in Statistics and Probability for Jefferson Abraham

For null hypothesis testing a requirement is a random and representative sample. Consider a population - A, A, A, A, A, A, A, A, B, B, B, B where A and B represent subjects in the population. A representative sample would be something like A, A, B. However why can we not choose a sample like A, B and then upweight the scores of A to make it representative of the population?