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 invegstigation 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.

Charlie’s sampling method is flawed in that he gathered responses only from his statistics class, which likely doesn’t represent the entire city’s demographics. This convenience sampling introduces bias, as his classmates may share similar household sizes, socioeconomic background, or other factors that won't reflect the general population. A truly simple random sample would require sampling from various parts of the city. In real-world applications, random sampling is vital in fields such as market research, public health, and political polling. For instance, if a company wants to understand consumer preferences, they can't just ask their employees! That could lead to skewed results. Instead, they should use a method that ensures every segment of their target audience has a chance to respond, leading to more trustworthy conclusions.