Interpreting Confidence Intervals EXPLAINED in 3 Minutes with Examples

Introduction to Interpreting Confidence Intervals

• Mark from Ace Tutors is going to explain how to interpret confidence intervals and why it can be confusing.

"I'm going to quickly explain how to interpret confidence intervals and why it's often so confusing."

Understanding an Example Scenario

• Let's say you want to estimate the average amount of sleep that everyone at your school gets per night.

• You took a sample of students and found that a 95% confidence interval for the true mean amount of sleep is 7.5 to 8.5 hours.

"To do this, you took a sample of students and found that a 95 confidence interval for the true mean amount of sleep is 7.5 to 8.5 hours."

Common Misconception

• Many students mistakenly think that there is a 95% chance that the true mean falls between 7.5 and 8.5 hours.

• This interpretation is actually wrong.

"What a lot of students say and understandably so is that there's a 95 chance that the true mean falls between 7.5 and 8.5 hours. This seems like it makes sense, but it's actually wrong."

Understanding Confidence Intervals

• The true mean is a specific constant value, but we don't know what it is.

• When we create a confidence interval, there's no certain chance or probability that it is inside or outside of that interval. It's either one or the other, with 100% certainty.

• Instead, a 95% confidence interval represents that if we repeatedly found confidence intervals from samples of this population, 95% of those intervals would contain the true mean value.

"The true mean is some specific constant value we don't know what it is, but we know it's a specific number. When we create our confidence interval, there's no certain chance or probability that is inside or outside of that interval. It's either one or the other, inside or outside with a hundred percent certainty. Instead, what a ninety-five percent confidence interval represents is that if we've repeatedly found confidence intervals from samples of this population like we did in this example, 95 percent of those intervals would contain the true mean value."

Dealing with Variability

• Each time we collect a sample, it will have a different mean, standard deviation, and sample size, leading to different intervals.

• However, as we calculate intervals again and again, 95% of them will include the population parameter, which in this case is the mean.

• This definition is the most correct one when it comes to interpreting confidence intervals.

"Every time you collect a sample, it will have a different mean, standard deviation, and sample size, so we'll end up with a different interval each time. However, as you calculate intervals again and again, 95% of them will include the population parameter, in our case, the mean."

Shorthand Version

• A shorthand version of this interpretation may say that we are 95% confident that the true mean is within 7.5 and 8.5 hours.

• Although it may seem similar to the first statement, math and stat people are very particular with their language.

"You may also see and use a kind of shorthand version of this statement, saying that we are 95 confident that the true mean is within 7.5 and 8.5 hours. Now, I know this looks very similar to the first statement, but math and stat people are very picky with their language."

Key Takeaway

• When interpreting confidence intervals, use the word "confident" instead of "chance" or "probability."

"If you only take one thing from this video, please remember whenever you interpret your confidence interval, use the word 'confident' instead of 'chance' or 'probability.'"

Conclusion

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