Below a description is given of several distributions. Drag the distribution plots on the right to the correct positions on the left. When your done, press the Check button at the bottom of this page, to check whether all plots are in the right place.

**Assumed distribution of the $y$ scores in the population:**

**Sampling distribution of the sample mean $\bar{y}$:**

What is the sampling distribution of the sample mean? Suppose that we would draw an infinite number of samples of size $N$ from the population, and in each sample we computed the sample mean of the scores on $y$. Different samples would result in different sample means, due to the randomness of the data. The distribution of all these sample means is the sampling distribution of the sample mean.

**Sampling distribution of the sample mean $\bar{y}$, if $\mu = \mu_0$ (i.e., if the null hypothesis were true):**

**Sampling distribution of $z = \frac{\bar{y} - \mu_0}{\sigma/\sqrt{N}}$, if $\mu = \mu_0$:**

**Sampling distribution of $t = \frac{\bar{y} - \mu_0}{s/\sqrt{N}}$, if $\mu = \mu_0$:**

**Probability of finding the observed $t$ value (red dot) or more extreme, if $\mu = \mu_0$ (two sided $p$ value):**

**Rejection region for two sided test, with significance level $\alpha$:**

**Choose from the images below:**