Estimating a Parameter from Sample Data: Process & Examples

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  • 0:01 Using Statistics to…
  • 0:46 Populations & Parameters
  • 1:51 Samples & Statistics
  • 3:07 Inferring Parameters…
  • 6:09 Lesson Summary
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Lesson Transcript
Instructor: Cathryn Jackson

Cat has taught a variety of subjects, including communications, mathematics, and technology. Cat has a master's degree in education and is currently working on her Ph.D.

One of the most useful things we can do with data is use it to describe a population. Learn how in this lesson as we discuss the concepts of parameters and samples.

Using Statistics to Understand Populations

Josephina is looking to start her own small business. She wants to call her business 'Puppy Paws' and sell shoes, socks, and booties to pets of all kinds. She needs to conduct some research to find out if her business will be successful in her town. However, she does not have time or the resources to talk to everyone in the town about her business. To gather information, Josephina will need to ask a sample and infer information about the population from the sample.

In this lesson, you will learn about the relationship between population and parameters, as well as the relationship between samples and statistics. Lastly, we will use this information to learn how to infer parameters about certain populations.

Populations & Parameters

To find out if her business will be successful, Josephina will need to understand the population of her town. A population is all members of a specified group. In this case, all of the citizens that live in Josephina's town are considered members of the target population. Josephina wants to know the mean number of pets that each person in the population owns.

When statisticians talk about mean, or average, they use the symbol called mu. Often, this mean, or average, is used to tell statisticians about the population they are studying. This is also known as a parameter. A parameter is a characteristic used to describe a population. Josephina needs to understand the characteristics of the population in order to understand if there is a need for her business. For example, if she finds that the pet ownership parameter of the town is .25 pets per person, then she knows that there are enough pets in the town for her business to be successful.

Now that you understand the relationship between population and parameters, let's discuss how they relate to samples and statistics.

Samples & Statistics

Since Josephina can't ask everyone in the town about her business, she will need to reach out to as many people as possible. This is called a sample, which is a part of a population used to describe the whole group. Josephina wants to know the average number of pets per person and the interest that each person has in providing footwear for their pets. To find this information without surveying the whole town, she can take a sample in many different ways. These include: random sampling, simple random sampling, cluster sampling , stratified sampling, and systematic sampling. You'll learn more about each of these types of sampling in future lessons!

First, Josephina wants to collect information about how many pets there are in the town, so she decides to go to a gathering place in the town and ask the people there about their pets. Since the dog park would give her biased information, she decides to survey people at a local movie theater. After she collects all of the information from the movie theater, she can create a statistic. A statistic is the characteristics of a sample used to infer information about the population. Of the people that Josephina surveyed, one in three own at least one pet. But how can we use this information to understand the population, since it only reflects the sample? We can do this by inferring parameters from our statistics.

Inferring Parameters from Statistics

Inferring parameters from statistics is pretty simple in this lesson. You will just take the statistic that you've found and use it to determine the parameter. In future lessons, you will learn more about the accuracy of your parameter, which is important. For example, if Josephina surveyed the people in the dog park about the number of pets they own, she would probably find that every person owned at least one pet. But we know this is probably not an accurate way to describe the entire population. We can determine how accurate a parameter is by using a concept called a confidence interval. That's a more complicated concept that we will discuss in a future lesson. For now, let's look at parameters in a more logical fashion.

Josephina wants to know if pet owners would be interested in footwear for their pets. She surveys people at the movie theater and at the dog park. Everyone is required to answer the question, even if they don't own a pet. Considering that Josephina's population is all pet owners in the town, which piece of information should she use to develop a parameter?

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