The population proportion and sample proportion always have the same value.
Choose the correct answer below. A. True B. False
The Correct Answer and Explanation is:
The correct answer is B. False.
To understand why this statement is false, we must first define the terms “population proportion” and “sample proportion.”
Population Proportion: This refers to the proportion of a certain characteristic in an entire population. For instance, if we consider a population of voters and want to know the proportion who support a particular candidate, that proportion (let’s say 60%) reflects the views of all voters in that population.
Sample Proportion: In contrast, the sample proportion is derived from a smaller subset of the population (the sample). It estimates the same characteristic as the population proportion, but due to random variation, the sample proportion can differ from the population proportion. For example, if a random sample of voters is taken, and 65% of that sample supports the candidate, the sample proportion is 0.65, which may not equal the population proportion of 0.60.
The difference between these two proportions arises primarily due to sampling error. Sampling error is the discrepancy between the sample statistic (the sample proportion) and the population parameter (the population proportion) that occurs because the sample does not perfectly represent the population. This discrepancy can be affected by several factors, including the sample size and how representative the sample is of the population.
In larger samples, the sample proportion tends to be closer to the population proportion due to the Law of Large Numbers, which states that as the size of the sample increases, the sample proportion will converge to the population proportion. However, it is still possible for the two proportions to differ due to random variation inherent in the sampling process.
In summary, while the population proportion is a fixed value representing the entire population, the sample proportion can vary from sample to sample, leading to the conclusion that they do not always have the same value.