To address the statement, "In my statistical study, I used a sample that was larger than the population," we need to understand the relationship between a population and a sample in statistics.
1. Population: This refers to the complete set of items or individuals that we are interested in studying. For instance, if a researcher is studying the heights of all high school students in a particular school, the population would be every high school student in that school.
2. Sample: A sample is a subset of the population. This means it is a smaller group selected from the population. For example, if the researcher selects 100 students from the school to measure their heights, those 100 students form the sample.
There are a few fundamental principles concerning populations and samples:
- A sample cannot exceed the size of the population, because by definition, a sample is a part of something larger. It is derived from the population.
- Hence, a sample being larger than the population is a logical impossibility.
Now, let’s examine each answer choice:
- A. No, the statement does not make sense. The sample size should always equal the population size.
- This is incorrect. The sample size does not have to equal the population size. The sample is typically smaller than the population.
- B. Yes, the statement makes sense. A sample can be as large as desired.
- This is incorrect. While you can choose how large you want your sample to be, it still cannot be larger than the population from which it is drawn.
- C. Yes, the statement makes sense. A sample is always larger than the population.
- This is incorrect. A sample cannot be larger than the population; it is a subset of the population.
- D. No, the statement does not make sense. A sample is a subset of the population and cannot be larger than the population.
- This is correct. Since a sample is a part of the population, it logically follows that it cannot exceed the size of the population.
Thus, the correct answer is:
D. No, the statement does not make sense. A sample is a subset of the population and cannot be larger than the population.
This answer provides a thorough explanation consistent with the principles of statistics, affirming that a sample drawn from a population must be smaller or at most equal to the size of the population.
