Question

as part of a statistics project, charlie would like to collect data on household size in his city. to do so, he asks each person in his statistics class for the size of their household and reports the results of a simple random sample. however, this is not a simple random sample. why?
charlie did not use any randomization; he took a convenience sample.
charlie did not use a random number table to randomize the order in which he collected the students responses, so the sample cannot be random.
in this investigation of household size, each household represents a case. charlie incorrectly sampled individuals instead of households.
both (a) and (c) are correct.
answers (a), (b), and (c) are all correct.

Explanation:

• Option (a): Charlie took a convenience sample (asking classmates) instead of using proper randomization methods like random number tables or random selection from the entire city's population.
• Option (b): Just because he didn't use a random - number table doesn't mean it's not a simple random sample. A simple random sample can be created using other randomization techniques (e.g., random digit dialing if it was a phone survey). So, this option is incorrect.
• Option (c): The variable of interest is household size. By sampling individuals (classmates), he is not sampling households. For example, two classmates could be from the same household.

Answer:

Both (a) and (c) are correct.