How To Find A Parameter In Statistics

What is a population parameter?

Jenn (B.S., M.Ed.) of Calcworkshop® teaching population parameter

Jenn, Founder Calcworkshop^®, 15+ Years Experience (Licensed & Certified Instructor)

That's exactly what you're going to larn in today's statistics lesson.

You'll learn how to calculate population parameters with eleven easy to follow step-past-step video examples.

Review of the basic terminology and much more!

And so hither we get…

How practice you acquire almost the nature of a population when you tin't feasibly examination every one or everything within a population?

Nosotros utilise a sample!

Although nosotros discussed sampling methods in our Exploring Data chapter, information technology's important to review some key concepts and dig a little deeper into how that impacts sampling distributions.

Let's jump in with some terminology.

Sample Statistics vs Population Parameters

When nosotros compute a statistical measures about a population we call that a parameter, or a population parameter. And when we compute statistical mensurate nearly a sample we call that a statistic, or a sample statistic every bit noted by Penn Land.

real world examples of a parameter population

Real World Examples of a Parameter Population

Think of information technology like this. Imagine you want to know if an apples is ripe and fix to eat. Then, you take a bite of the apple to see if it's good. If the apple tree tastes crunchy, and so you can conclude that the rest of the apple will too be crunchy and good to eat. But if the bite from the apple is mushy, then you can infer that the rest of the apple is mushy and bad to eat. Hence, the bite from the apple is a sample statistic, and the conclusion you draw relates to the entire apple, or the population parameter.

Nosotros typically use Greek letters like mu and sigma to identify parameters, and English language messages like x-bar and p-hat to identify statistics.

parameter vs statistic

Parameter Vs Statistic

Sampling Fault

Now, with all samples, surveys, or experiments, there is the possibility of error. Sampling fault is the error that occurs considering of take chances variation. Information technology's the difference betwixt a statistic and parameter (i.e., the difference between the sample and the population). The best fashion to reduce sampling error is to increment the sample size.

Some errors tin occur with the choice of sampling, such every bit convenient sampling, or in the response of sampling, such as those errors that we can accumulate with drove or recording of data. This type of error is called non-sampling error.

Sampling Distribution

But why do we care?

Well, nosotros hope to draw inferences nearly probability distributions by analyzing sampling distributions.

A sampling distribution is a probability distribution obtained from a larger number of samples fatigued from a specific population. In other words, it'southward the distribution of frequencies for a range of dissimilar outcomes that could occur for a statistic of a given population.

If we know that the population distribution is normal, so the sampling distribution volition also be normal, regardless of the size of the sample. If the population is not normal, meaning it'southward either skewed right or skewed left, then we must apply the Fundamental Limit Theorem.

What Is The Cardinal Limit Theorem?

The Central Limit Theorem (CLT) states that if a random sample of n observations is drawn from a non-normal population, and if n is big enough, and so the sampling distribution becomes approximately normal (bell-shaped). In other words, the central limit theorem allows u.s. to accurately predict a population's characteristics when the sample size is sufficiently large.

central limit theorem definition

Primal Limit Theorem — Definition

Put another way, if we have a large plenty sample, then the sampling distribution becomes approximately normal. Nosotros can use all of our onetime tricks to find probability similar z-scores and z-tables!

So, what is our ultimate goal?

We want to find an advisable sample statistic, either a sample mean or sample proportion, and decide if it is a consistent estimator for the populations as a whole.

sample proportion properties

Sample Proportion Properties

sample mean properties

Sample Mean Properties

How To Find Population Parameters

For example, suppose a highway construction zone, with a speed limit of 45 mph, is known to have an boilerplate vehicle speed of 51 mph with a standard departure of five mph, what is the probability that the mean speed of a random sample of 40 cars is more than than 53 mph?

population parameter example

Population Parameter — Example

Together, we will look at how to find the sample mean, sample standard departure, and sample proportions to help united states create, study, and analyze sampling distributions, only similar the example seen higher up.

Population Parameter – Lesson & Examples (Video)

one hr eleven min

Introduction to Video: Sample Ways and Sample Proportions
00:00:37 – What is the departure between a parameter and a statistic? with Example #1
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00:09:07 – Identify the parameter and statistic for the following scenarios (Examples #2-4)
00:14:09 – Create a population distribution and a sampling distribution (Example #v)
00:21:47 – What is the divergence between sampling error and non-sampling error?
00:28:19 – Given the sample data discover the sample mean and sample standard deviation (Example #half-dozen)
00:31:26 – Properties of Sampling Distribution for Sample Means, Illustrations and the Central Limit Theorem
00:37:47 – Find the probability for an approximately normal distribution using sample ways(Example #seven-8)
00:49:45 – Properties of Sampling Distributions for Sample Proportions with Example #nine
00:59:48 – Discover the probability for an approximately normal distribution using sample proportions (Examples #10-12)
Practice Problems with Pace-by-Step Solutions
Chapter Tests with Video Solutions