Question

1. as part of a statistics project, andrea would like to collect data on household size in her city. to do so, she asks each person in her statistics class for the size of their household, and reports that her sample is a simple random sample. however, this is not a simple random sample. which of the following is the best reasoning for why this is not a random sample that is appropriate for this research question?

andrea did not block for any variables that might influence the response.

andrea did not use a stratified sample.

andrea did not use any randomization; she took a convenience sample.

Explanation:

To determine why Andrea's sample is not a simple random sample, we analyze each option:

1. Blocking is used in experimental design (like in experiments with treatments), not in sampling for observational data (collecting household size). So the first option is incorrect.
2. A stratified sample is a type of sampling where the population is divided into groups (strata) and samples are taken from each. But the issue here is not about not using stratified sampling, but about the lack of randomization in selecting the sample. So the second option is incorrect.
3. Andrea asked people in her statistics class, which is a convenience sample (using easily accessible subjects) and there was no randomization (like randomly selecting households from the city's population). A simple random sample requires that every member of the population (all households in the city) has an equal chance of being selected, which is not the case here as she just used her class (a non - random, convenient group).

Answer:

Andrea did not use any randomization; she took a convenience sample.