Suppose we have a confidence interval of and the error bound is 549.5 .
What was the value of the sample mean?
Enter your answer

To find the sample mean from the confidence interval , you can use the formula for the midpoint of the interval. The sample mean is calculated as:

So, .

Now let’s have some fun facts about confidence intervals!

When constructing a confidence interval, you’re essentially trying to capture the true population parameter (like the mean) with a certain level of precision. The width of the interval depends on the variability of the data and the sample size. A larger sample size tends to yield a narrower confidence interval, which gives you a more precise estimate!

If you’re ever using confidence intervals in real-world scenarios, remember that they are not black and white! A 95% confidence interval means you can expect that if you were to take multiple samples and build intervals, about 95% of those would contain the true population mean. So, there’s still a 5% chance your estimate could miss the target!