Chapter 8: Estimating with Confidence - Confidence Intervals: The Basics

Confidence Intervals: The Basics

What is a Confidence Interval?

• A confidence interval gives a range of values that we think contains the true average of something, like people's heights or test scores.

• For example, if we say the average height is between 5'5" and 5'9", we are saying we are pretty sure the true average height is somewhere in that range.

How Do We Make a Confidence Interval?

• First, we take a small group (a sample) and measure something, such as their heights. Let's say our sample averaged 5'7".

• We then add and subtract a small number (called the margin of error) to create our range.

  • Example: If the margin of error is 2 inches, then our confidence interval would be:

  • 5'7" - 2 inches = 5'5"

  • 5'7" + 2 inches = 5'9"

  • So, we say the average height is between 5'5" and 5'9".

What is the Confidence Level?

• The confidence level tells us how sure we are about our interval. If we say we are 95% confident, it means if we did the same experiment 100 times, about 95 out of 100 times, our interval would contain the true average.

Why Are Confidence Intervals Important?

• Confidence intervals help us understand the uncertainty in our estimates. They tell us that samples may not give us the exact average but rather a good guess.

• It’s important to consider how we collect our samples (they should be random) to ensure our interval is reliable.

Key Points to Remember:

• A confidence interval gives a range of likely values for an average.

• It is created by taking a sample and using a margin of error.

• The confidence level shows how sure we are about the interval containing the true average.