Final answer:
A 95% confidence level signifies that if numerous confidence intervals were constructed from separate samples, 95% of them would contain the true population mean height. It means there is a high degree of certainty that the population mean lies within the calculated interval, yet it does not mean that 95% of the data falls within this interval.
Step-by-step explanation:
Explanation of 95 Percent Confidence Level
When we talk about a 95% confidence level in the context of estimating the average height, we are referring to the degree of certainty in statistical inference. This confidence level tells us that if we were to take many samples and construct confidence intervals for each sample, we would expect 95% of those intervals to contain the true population mean height. It is important to note that the 95% confidence level does not imply that 95% of the data lies within the interval that you calculated.
As an example, if you have a 95% confidence interval for the average height of male Swedes, such as (67.02 inches, 68.98 inches), this interval estimatess where the true population mean likely falls. The width of the interval, which in this case is wider than the 90% confidence interval, indicates the precision of our estimate; a wider interval suggests less precision, but greater confidence that it contains the population mean.
When you construct a 95% confidence interval using sample data, you are using statistical methods to estimate a range that you are 95% confident includes the true population mean. This estimation is under the assumption that the sampling method is sound and the data is representative of the population. It's a way to express uncertainty about the estimate being made.