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.

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.

Transcript text: 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

Solution Steps

I'm here to help with Python-related questions or tasks. If you have a specific math problem or need assistance with Python code, feel free to ask!### Step 1: Understand the Problem The problem is asking us to identify why Charlie's method of collecting data is not a simple random sample. We are given several options to choose from, and we need to determine which one(s) correctly explain the issue with Charlie's sampling method.

Step 2: Analyze Each Option

Option (a): Charlie did not use any randomization; he took a convenience sample.
- A simple random sample requires that every member of the population has an equal chance of being selected. By taking a convenience sample, Charlie is selecting individuals based on ease of access rather than randomization, which violates the principles of a simple random sample.
Option (b): 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.
- While using a random number table is one method to ensure randomization, the lack of using such a table does not inherently mean the sample is not random. There are other ways to achieve randomization.
Option (c): In this investigation of household size, each household represents a case. Charlie incorrectly sampled individuals instead of households.
- The investigation is about household size, so the unit of analysis should be the household, not individual students. By sampling individuals, Charlie is not accurately representing the population of interest, which is households.

Step 3: Determine the Correct Answer

Option (d): Both (a) and (c) are correct.
- This option suggests that both the lack of randomization and the incorrect unit of analysis are issues with Charlie's sampling method.
Option (e): Answers (a), (b), and (c) are all correct.
- This option suggests that all three issues are present. However, as discussed, option (b) is not necessarily a valid reason for the sample not being random.

Final Answer

The correct explanation for why Charlie's method is not a simple random sample is that he did not use any randomization and incorrectly sampled individuals instead of households. Therefore, the answer is:

\[ \boxed{\text{Both (a) and (c) are correct.}} \]

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