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MTH 203 Assistant
I'm trying to understand confidence intervals. I know it's about ranges, but why do we use them instead of just one number like a mean?
Sure, let's walk through it. A confidence interval gives a range where we're fairly certain the true population value lies. A single number, like the mean from a sample, doesn't capture the uncertainty. The interval shows how precise your estimate is and reflects how much the data can vary.
For example, saying "the average test score is 78" tells you one thing—but saying "we're 95% confident the average is between 75 and 81" gives more useful context. It acknowledges sampling variability and gives a clearer picture of what we might expect in the broader population.
So the wider the interval, the less confident we are?
Close! Actually, the width of the interval reflects the precision of your estimate. A wider interval usually means less precision, possibly because of a small sample size or more variability in your data.
But you can still have a 95% confidence even with a wide interval. It just means you're confident the true value is in a broader range. Narrower intervals indicate more precision—but you always need to interpret them in context.
Be sure to compare the confidence intervals from two different sample sizes in this week’s lab. It'll help you see how more data tightens those intervals. And don’t forget: just because two intervals overlap doesn’t always mean the difference isn't significant—watch for that nuance in the quiz.
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