### Statistical Inference for $\mu_1-\mu_2$

 $n_1=$ $\bar{x}_1=$ s₁= σ₁= $n_2=$ $\bar{x}_2=$ s₂= σ₂= Assume: σ₁ = σ₂ σ₁ ≠ σ₂

CI for $\mu_1 - \mu_2$:

$H_0:\mu_1-\mu_2$
$H_a:\mu_1-\mu_2$

Significance level: $\alpha =$

Show equations

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

#### Assume

1. $X_{1i} \stackrel{iid}{\sim} N(\mu_1,\sigma_1^2)$ for $i=1,\ldots,n_1$
2. $X_{2i} \stackrel{iid}{\sim} N(\mu_2,\sigma_2^2)$ for $i=1,\ldots,n_2$
3. 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.