### Statistical Inference for $\mu$

 $n=$ $\bar{x}=$ s= σ=

CI for $\mu$:

$H_0:\mu$
$H_a:\mu$

Significance level: $\alpha =$

Show equations

This applet computes performs inference for a population mean $\mu$.

#### Assume

$X_i \stackrel{iid}{\sim} N(\mu,\sigma^2)$ for $i=1,\ldots,n$

#### Directions

• Enter the sample size in the $n$ box.
• Enter the sample mean in the $\bar{x}$ box.
• Enter either the population standard deviation $\sigma$ or the sample standard deviation $s$ in the standard deviation box.
• Hitting "Tab" or "Enter" on your keyboard will compute a 95% confidence interval for $\mu$ (you can change the confidence level using the drop-down box).

To perform a hypothesis test for $\mu$, enter $H_0$ and $H_a$. Specify the null and alternative hypotheses with the drop-down boxes. The critical value, rejection region, test statistic, and $p-$value are computed and graphed. Different significance levels can be chosen with the drop-down box.