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

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?

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

You can still ask an expert for help

SofZookywookeoybd

Answered 2022-04-01
Author has **15** answers

Hint: The $1-\alpha$ confidence interval for $\mu$ is

$\left\{\begin{array}{cc}\stackrel{\u2015}{X}-{z}_{(1-\frac{\alpha}{2})}\cdot \frac{\sigma}{\sqrt{n}}& \stackrel{\u2015}{X}+{z}_{(1-\frac{\alpha}{2})}\cdot \frac{\sigma}{\sqrt{n}}\end{array}\right\}$

$z}_{(1-\frac{\alpha}{2})$ is the z-value of the standard normal distribution. $1-\alpha$ is the confidence level.

In your case $\stackrel{\u2015}{X}=37.28,\sigma =34\text{}\text{and}\text{}1-\frac{\alpha}{2}=1-\frac{0.01}{2}=0.995$.

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