eterna said:Homework Statement
What does it mean?
Does this mean that 95% of the means from a sample mean distribution (frequency distribution of means of sample size n) are a certain number of standard deviations from the population mean?
Homework Equations
The Attempt at a Solution
Ray Vickson said:A 95% confidence interval is an interval that has a 95% chance of overlapping the true, unknown population mean μ. In other words, if you were to repeat the sampling experiment many times you would get many different intervals, but about 95% of them would contain the true mean somewhere inside them. See, eg., http://en.wikipedia.org/wiki/Confidence_interval and look especially at the section entitled "Meaning and Interpretation".
eterna said:so was what I said a completely wrong way of thinking about it?
A 95% confidence interval on the mean is a range of values calculated from a sample of data that is likely to contain the true population mean with 95% confidence. This means that if we were to take multiple samples from the same population, 95% of the time the calculated confidence interval would contain the true population mean.
A 95% confidence interval on the mean is calculated by taking the sample mean and adding and subtracting the margin of error. The margin of error is determined by the sample size, standard deviation, and desired level of confidence. This calculation is based on the Central Limit Theorem, which states that the sample mean will be normally distributed around the population mean.
A 95% confidence interval is commonly used in statistical analysis because it provides a good balance between precision and reliability. It gives a narrow range of values that are likely to contain the true population mean, while still allowing for some margin of error.
The 95% confidence level refers to the level of certainty that the calculated confidence interval contains the true population mean. It means that if we were to take multiple samples from the same population, 95% of the time the calculated confidence interval would contain the true population mean.
A 95% confidence interval can be interpreted as a range of values within which we are 95% confident that the true population mean lies. This means that if we were to take multiple samples from the same population and calculate a confidence interval for each sample, 95% of those intervals would contain the true population mean.