Intro to Confidence Intervals (lesson)

Confidence Intervals

I can create a confidence interval to reflect a true parameter of a population in context

Vocabulary

• Point Estimate

• Confidence interval

• Margin of Error

• Small Sample Size n<30 (1-29)

• Large Sample Size n=30+ (30 or more)

Multiple Choice

Find the mean of these five prob/stats test grades:

50, 76, 81, 70, 92

• 81

• 76.3

• 73.8

• 260

Multiple Choice

Identify the sample from the previous question

• ALL prob/stats test grades

• 5 randomly selected prob/stats test grades

Multiple Choice

Identify the population of the previous question

• ALL prob/stats test grades

• 5 randomly selected prob/stats test grades

Multiple Choice

Identify the sample mean

• 73.8

• we did not find the sample mean

Multiple Choice

Identify the population mean

• 73.8

• we did not find the population mean

Point estimate

73.8 is going to be our point estimate to represent the true mean of the population of ALL prob/stats test grades. Recall that this was our sample mean.

Confidence interval

Now we must make our confidence interval of our point estimate by determining a margin of error. The margin or error is usually a small number that allows for miscalculations or "wiggle" room so to speak for your true mean or true proportion estimate of the population.

Let's choose, for example, a margin of error of 5 points for our problem.

Multiple Choice

Now subtract your margin of error from the point estimate 73.8. This is the lower end of your interval. Next, add your margin of error to the point estimate of 73.8. This is the upper end of your confidence interval. What is your interval?

• 68.8 - 78.8

• 63.8 - 83.8

• 58.8 - 88.8

We can now say, with a certain amount of confidence, that the population mean would fall somewhere between these two numbers. That is really all we can claim.

Let's practice

One of the samples had two scores of 71 and 79. To find the point estimate of these scores, find the mean.

Multiple Choice

What is the point estimate of 71 and 79?

• 71

• 78

• 75

• 150

Margin of error

In this case to find the margin of error we would subtract the smaller number from the larger number and divide by 2. In other words what is the "wiggle room" on each side of the mean?

Multiple Choice

What is the margin of error of the sample 71 and 79?

• 2

• 4

• 6

Multiple Choice

What is the confidence interval?

• 71-75

• 75-79

• 71-79

• 67-83

Multiple Choice

A group of students claims that the true population mean of scores is 84.

Does the previous interval we found support or deny this claim?

• yes, 84 is within my interval

• no, 84 is not within my interval

Summary

-A point estimate is how we use a statistic to guess a parameter

-Margin of error is a number that allows for miscalculations

-Confidence interval is an interval of values in which our true parameter could lie.