How to compute a 95 confidence interval for the population mean?

There are three common methods for calculating sample population means: the simple average, the mean of the trimmed mean, and the Hodges-Lehmann estimator. Each method provides a slightly different result.

4

If you have a large sample size (more than 30), you can use a normal approximation for the sample mean. This is a very accurate estimate when the sample size is large. A normal (or z) distribution is symmetric around its mean value. This means that 68% of the values will be found within a range that is either one standard deviation below or above the mean. A 95% confidence interval is a range within which you can be 95% sure that the population mean lies. A

How to calculate a 95% confidence interval for the population mean if you don't know the population variance?

If you don't know the population standard deviation (or variance), there is no simple way to find the population mean and a 95% confidence interval. However, there are ways to approximate these statistics.

How to calculate a 95% confidence interval for the population mean?

We use the sample mean, to describe the population mean. The sample mean is the sum of the values of the sample divided by the number of observations in the sample. It is a single number representing the population mean. In the previous example, we estimated the population mean of the height of silver spruce trees in Maine to be 68.8 inches. If we repeated this process 100 times, the sample mean would be 68.8 inches most of the time. But if the sample mean was

How to calculate a 95% confidence interval for the population mean with sample mean?

If we have a sample of size $n$, the standard error of the sample mean is $\frac{s}{\sqrt{n}}$. So, if we want to use the sample to calculate a confidence interval for the population mean, we use the following formula: $P(X_n - Z_{1 - \frac{\alpha}{2}} \leq \bar{X} \leq X_n + Z_{1 - \frac{\alpha}{2}}