Inference for μ₁-μ₂

Statistical Inference for $\mu_1-\mu_2$

Assume:

CI for $\mu_1 - \mu_2$:

Significance level: $\alpha =$

Show equations

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

Assume

$X_{1i} \stackrel{iid}{\sim} N(\mu_1,\sigma_1^2)$ for $i=1,\ldots,n_1$
$X_{2i} \stackrel{iid}{\sim} N(\mu_2,\sigma_2^2)$ for $i=1,\ldots,n_2$
Samples are independent

Directions

For the first sample, enter the sample size in the $n_1$ box, enter the sample mean in the $\bar{x}_1$ box, and enter either the population standard deviation $\sigma_1$ or the sample standard deviation $s_1$ in the standard deviation box.
Enter the summary statistics for the second sample.
For a two-sample t-test (i.e. when entering $s_1$ and $s_2$), choose if you are assuming $\sigma_1 = \sigma_2$ or $\sigma_1 \neq \sigma_2$ from the drop-down box.
Hitting "Tab" or "Enter" on your keyboard will compute a 95% confidence interval for $\mu_1-\mu_2$ (you can change the confidence level using the drop-down box).

To perform a hypothesis test for $\mu_1-\mu_2$, 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.