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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 + 25/√25 =42 Am i correct?

Nobi
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  • Formatting tips here. – Em. Mar 20 '16 at 14:19
  • If you're actually given the population mean, then that's what you should use for the population mean. This doesn't usually happen, though. When it doesn't, the sample mean is a point estimator (a single randomly chosen number which is usually close to the population mean). A confidence interval is an interval estimator (a randomly chosen interval which usually contains the population mean). Both of these are commonly used. – Ian Mar 20 '16 at 14:21
  • Yeah but in my case I think i need to find the population mean to solve my question. Here is my question. Suppose that population sd of this waiting time is 34 minutes. Construct a 99% confidence interval for the true mean waiting time. – Nobi Mar 20 '16 at 14:25

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

$$\large{\left[ \overline X-z_{(1-\frac{\alpha}{2})} \cdot \frac{\sigma}{\sqrt n} , \overline X+z_{(1-\frac{\alpha}{2})} \cdot \frac{\sigma}{\sqrt n}\right]}$$

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

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

callculus42
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