Determining the Sample Size to Estimate Confidence Intervals: Definition & Process

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  • 0:01 Sample vs. Census
  • 0:51 Determining the Sample Size
  • 1:33 Example
  • 3:33 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov

Artem has a doctor of veterinary medicine degree.

In this lesson, you will learn how to determine the most appropriate sample size to find the confidence interval we need using a specific case example.

Sample vs. Census

Do you know why research companies usually conduct sample surveys instead of an entire census? Time and money! There is only so much time and money around, and perhaps personnel. Imagine trying to weigh every person in the U.S. to figure out the average weight of an American. That would be crazy!

This is why a smaller sample is usually adequate enough to find out such information without having to take a larger sample. Let's look at out how we determine what sample size we need with respect to the confidence interval we are looking for.

A confidence interval is the point estimate +/- the margin of error, and the point estimate is the value of a sample statistic, which is used as an estimate of a population parameter. The number added to or subtracted from the point estimate is known as the margin of error.

Determining the Sample Size

To determine the sample size we need, we can turn to the following equation:

n = (z2 * sigma2) / (E2)

Here, n is the sample size, E is the margin of error, sigma is the population standard deviation, and the value for z is found from standard normal distribution tables for the appropriate given confidence level at the back of most statistics books.

In case we don't know what the population standard deviation (sigma) is, we can then take a preliminary sample and find the sample standard deviation (s) and use that instead of sigma in the formula I just described.

Example

Ok. That's all you really need to know at this point. Let's work through everything with an actual example.

A research company wants to figure out the mean salary of 30-year-old people in the U.S. It's known that sigm', the population standard deviation, is equal to $5,000. What should our sample size be so that the estimate with a 99% confidence level is within $500 of mu, the population mean?

Let's break this down.

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