Repeated Sampling

Suppose the samples of same size are repeatedly taken from a population that follows a normal distribution with a mean of $M$ and a standard deviation of $S$. the means of samples will be normally distributed with a mean of $M$ and a standard deviation

$\alpha$ is the probability of error which the researcher is willing to accept $1-\alpha$ = Confidence Level $S$ is $\sigma$. Standard Deviation $M$ is $\mu$ Average

Formulas

${\sigma }_{\overline{x}}=\frac{\sigma }{\sqrt{n}}$ $E=\frac{z\sigma }{\sqrt{n}}$ $E=z{\sigma }_{\overline{x}}$