Determine whether the number describes a population parameter ...

Question

Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning.

Voter registration records show that 47% of all voters in a county are registered as Democrats.

Accepted Answer

Below there. Today we're gonna solve the following practice problem together. So first off, let us read the problem and highlight all the key pieces of information that we need to use in order to solve this problem. A study of all residents in a neighborhood found that 62% on a bicycle. Is this 62% a population parameter or a sample statistic? Justify your answer. Awesome. So it appears for this particular problem we're asked to give our answer for whether or not this 62% is considered a population parameter or a sample statistic, and to justify our answer, and we're asked to accomplish this by using our information that is provided to us by the problem itself as context clues. So with that said, Looking at our multiple choice answers, let's read them off to see what our final answer might be. A is population parameter because it is derived from a random sample. B is sample statistic because it is obtained from a group of bicycle owners. C is population parameter because it represents the entire neighborhood, and D is sample statistic because it is based on a sample of residents. Awesome. So our first step in order to solve this particular problem is we need to recall and understand our two different concepts for population parameter and sample statistic. So I'll call population parameter PP for short and sample statistic as SS for short. So, as you should recall, the definitions for the population parameter and the sample statistic are as follows. A population parameter is a numerical value that represents a characteristic of the entire population as a whole, whereas a sample statistic is a numerical value that represents a characteristic of a subset. Which means a sample of the larger population as a whole. So what does that mean? So let's say we have a population of 600, and we take a sample of that population, and the sample is 300, so a sample is just a smaller piece of the larger population as a whole. So with that in mind, Now that we know the difference between a population and a sample, our second step is we need to identify the key information that we need to use in order to make our final decision whether or not the 62% is a population parameter or a sample statistic. So let us recall and note that the problem itself states that the study was conducted among all residents of the neighborhood. That is very important, that is key. A study of all the residents in a neighborhood. And our second key piece of information that we need to focus on is that the 62% represents the proportion of residents who own a bicycle. So our third and final step is we need to make our final conclusions. So therefore, without a doubt, since the data is collected from the entire population of residents as a whole, Rather than just a sample of these resident population, the 62% represents a population parameter, so that means our final answer, without a doubt has to be multiple choice answer letter C, which once again is population parameter because it represents the entire neighborhood. And that's it, we've officially solved for this problem. Thank you so much for watching. Hopefully that helped and I can't wait to see you in the next video. Bye.

Determine whether the number describes a population parameter or a sample statistic. Explain your reasoning.
Voter registration records show that 47% of all voters in a county are registered as Democrats.

Key Concepts

Population Parameter

Sample Statistic

Voter Registration Records

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