Question

Professor Whyte would like to determine how students feel about the implementation of a new fee that all students in the university are required to pay. She decides to sample 40 students. She assigns a number (between 1 and 200 inclusive) to all 200 students in her class such that no student has the same number. Then, she uses Excel to randomly choose 40 numbers between 1 and 200 (no repeated numbers).

(a) Is this an example of a simple random sample or a convenience sample? State the reason for your answer.

(b) State one benefit of the sampling method used by Professor Whyte.

(c) State one disadvantage of the sampling method used by Professor Whyte.

Answer 1

(a) This example of an experiment by Professor Whyte is an example of a simple random sample because here she is randomly choosing 40 numbers from among the 200 numbers that she assigned to all the 200 students of her class, where each student bears a different number.
(b) Using the simple random sampling method, we are able to easily generate samples, which are representative of the overall population.
(c) Using the simple random sampling method, we may require a large sample size if our given population is large. The sample size should be ideally 10% of the population size. If we take a small random sample, then the chances of having sampling error and bias will increase significantly.