### Video Transcript

Can a biased sample chosen from a given population be a stratified random sample?

To answer this question, let’s look at the definitions of the two ideas we want to compare; that’s a biased sample and a stratified random sample. A biased sample occurs when the sample is selected from a group that is not representative of the population.

Let’s consider an example. Suppose we have a region consisting of rural areas, suburban areas, and the inner city. And suppose that the regional council want to do a survey on pet ownership in their region. A questionnaire is sent to a random sample of inner-city households. But since the sample consists of only inner-city households, the sample is biased. That’s because neither the rural nor the suburban households are represented. And so this is a biased sample.

Now, let’s consider how we define a stratified random sample. We use stratified random sampling when the population is divided into nonoverlapping groups or strata. A random sample proportionate to the size of the stratum within the population is taken from each stratum and combined into one representative sample. The makeup of the population is then fully represented within the sample.

Suppose in our regional survey, the population consists of 50 percent of suburban, 20 percent rural, and 30 percent inner city households. Then a stratified random sample would also consist of 30 percent inner city, 50 percent suburban, and 20 percent rural households. The stratified random sample would have the same proportions as the whole region.

To conclude then, since a biased sample does not represent the population and a stratified sample does represent the population, then a biased sample cannot be a stratified random sample. Our answer is therefore no.