Example: Confidence Intervals

Imagine you’re a researcher trying to work out how many burglaries happen in a big city each month. It’s impossible to count every single burglary, so you decide to look at 100 neighbourhoods and count the burglaries there.

After your study, you find that on average, there are about 12 burglaries per neighborhood each month. But you know this number might not be exactly right for the whole city.

This is where confidence intervals come in handy. They help you say how sure you are about your findings.

Using some statistical tools (don’t worry about the maths!), you calculate something called a “95% confidence interval.” This gives you a range of numbers that you’re pretty sure includes the true average for the whole city.

Your results might look like this: “We are 95% confident that the average number of burglaries per neighbourhood in the entire city is between 11 and 13 per month.”

What does this mean in simple terms?

1. Your best guess is still 12 burglaries per neighbourhood.
2. But you’re acknowledging that it could be a bit less (as low as 11) or a bit more (as high as 13).
3. You’re pretty sure (95% sure, in fact) that the true average for the whole city falls somewhere in this range.

Why is this useful?

• It gives city officials a good idea of the burglary situation without having to count every single crime.
• They know the problem is likely not as low as 10 burglaries per neighbourhood or as high as 15.
• This helps them plan police patrols and crime prevention strategies more effectively.

The confidence interval is like saying, “We’re not exactly sure, but we’re pretty confident it’s in this range.” It’s a way of being honest about what we know and what we’re still uncertain about in our research.