Questions: 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.

Solution Steps

To determine why Charlie's sample is not a simple random sample, we need to evaluate the given options and identify the correct reasons. A simple random sample requires that every member of the population has an equal chance of being selected. We will analyze each option to see if it violates this principle.

1. Option (a) states that Charlie did not use any randomization and took a convenience sample. This is correct because a convenience sample is not random.
2. Option (b) mentions the use of a random number table, which is not necessary for a simple random sample, so this option is not relevant.
3. Option (c) indicates that Charlie sampled individuals instead of households, which is also correct because the unit of analysis should be households, not individuals.
4. Option (d) combines (a) and (c), which are both correct.
5. Option (e) includes (a), (b), and (c), but (b) is not relevant.

Thus, the correct answer is option (d).

To determine why Charlie's sample is not a simple random sample, we need to evaluate the definitions and characteristics of a simple random sample. A simple random sample requires that every member of the population has an equal chance of being selected.

We analyze the provided options:

• Option (a): Charlie did not use any randomization; he took a convenience sample. This is correct because a convenience sample does not ensure randomness.
• Option (b): Charlie did not use a random number table to randomize the order of responses. This is irrelevant to the definition of a simple random sample.
• Option (c): Charlie incorrectly sampled individuals instead of households. This is also correct, as the unit of analysis should be households.
• Option (d): Both (a) and (c) are correct. This option correctly identifies the issues with the sampling method.
• Option (e): Answers (a), (b), and (c) are all correct. This is incorrect because option (b) is not relevant.

From the analysis, options (a) and (c) are valid reasons for why the sample is not a simple random sample. Therefore, the correct answer is option (d).

Final Answer