 # Sample mean to population mean How to use sample Paula Good 2022-03-31 Answered
Sample mean to population mean
How to use sample mean to know the population mean? Now I have sample mean, sd and population mean. They are 37.28, 25 and 34. Sample size is 25 Here is my thought $N<25$. Sample mean may not equal to population mean. population mean is $37.28+\frac{25}{\sqrt{25}}=42$ Am i correct?
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Hint: The $1-\alpha$ confidence interval for $\mu$ is
$\left\{\begin{array}{cc}\stackrel{―}{X}-{z}_{\left(1-\frac{\alpha }{2}\right)}\cdot \frac{\sigma }{\sqrt{n}}& \stackrel{―}{X}+{z}_{\left(1-\frac{\alpha }{2}\right)}\cdot \frac{\sigma }{\sqrt{n}}\end{array}\right\}$
${z}_{\left(1-\frac{\alpha }{2}\right)}$ is the z-value of the standard normal distribution. $1-\alpha$ is the confidence level.