What is meant by the 95% confidence interval of the mean?
From Google:
The 95% confidence interval defines a range of values that you can be 95% certain contains the population mean. With large samples, you know that mean with much more precision than you do with a small sample, so the confidence interval is quite narrow when computed from a large sample.
The 95% confidence interval of the mean is a range of values within which we estimate the population mean to lie with 95% confidence. In other words, it gives us a range of values that we're pretty sure contains the true population mean.
To calculate the 95% confidence interval, we need three pieces of information: the sample mean, the sample size, and the population standard deviation (or the sample standard deviation if the population standard deviation is unknown).
Here are the steps to calculate it:
1. Take a random sample from the population of interest.
2. Calculate the sample mean (x̄) and the sample standard deviation (s).
3. Determine the critical value for a 95% confidence level. This value depends on the sample size and the desired confidence level, and it can be obtained from a standard statistical table or using a calculator.
4. Use the formula: Confidence Interval = x̄ ± (critical value * (s/√n))
- x̄ represents the sample mean
- critical value represents the value obtained in step 3
- s represents the sample standard deviation
- n represents the sample size
By plugging in the values from your sample into this formula, you'll obtain a range of values that constitutes the 95% confidence interval of the mean. This range can then be interpreted as the interval within which we estimate the true population mean to lie with 95% confidence.