Final answer:
A 95% confidence interval of (10 ± 4) suggests there is a 95% chance that the true population mean lies between 6 and 14. This interval is based on the sample data and implies that with repeated sampling, 95% of such intervals would contain the true mean μ. The confidence level indicates the proportion of intervals that would contain μ if sampling were repeated.
Step-by-step explanation:
When we say that a 95% confidence interval for a population mean μ is (10 ± 4), it means that there is a 95% chance that the true mean of the population lies between 6 and 14. This interval is calculated from a random sample of data and is used to estimate the parameter μ of the population from which the sample was drawn. It's important to note that this does not imply that the true population mean will definitely be within this range; rather, if we were to take multiple samples and construct a confidence interval from each one, we would expect about 95% of those intervals to contain the true population mean μ.
The 'confidence level' represents the percentage of confidence intervals that would contain the true population parameter μ if we took repeated samples. If our confidence level is 90%, then we can say that approximately 90%of the confidence intervals calculated from those samples would contain the true value of the population mean μ.
In summary, the confidence interval provides a range within which we can expect the true population mean to lie with a certain level of confidence, assuming that the sampling method is unbiased and that all other assumptions of the underlying statistical method are met.