## Related questions with answers

Suppose that, for a sample of size $n=100$ measurements, we find that $\bar{x}=50$. Assuming that $\sigma$ equals $2$, calculate confidence intervals for the population mean $\mu$ with the following confidence levels:

$97\%$

Solutions

VerifiedThe formula for the confidence interval for the population mean is given below,

$\bar{X}\plusmn Z_{\frac{\alpha}{2}}\dfrac{\sigma}{\sqrt{n}}=\left(\bar{X}-Z_{\frac{\alpha}{2}}\dfrac{\sigma}{\sqrt{n}},\bar{X}+ Z_{\frac{\alpha}{2}}\dfrac{\sigma}{\sqrt{n}}\right)$

$\bar{X}$ is the sample mean, $n$ is the sample size, and $Z_{\frac{\alpha}{2}}$ is the critical value from the standardized normal distribution.

To compute what is required, let's first determine all values we have from the task. It is known that the size of the sample is $100$ measurements, so $n=100.$ Also it is known that the sample mean is $50$, $\=x=50.$ Standard deviation amounts $2$, $\sigma=2$.

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