Assume a teacher constructs a four-choice multiple choice test. Each item has only one correct response. The test is scored from 0 to 100 representing the percentage of items answered correctly.
I want to have some rules of thumb that could be informative regarding how many items are required to achieve a given standard error of measurement. For example, it would be nice to be able to advice teachers who write their own multiple choice exams "if you have 100 items that are reasonably well worded, you can expect a standard error of measurement of 2.5".
The standard error of measurement is often defined as:
$$s_e=s_x \sqrt{1-r_{xx}}$$
where $s_x$ is the standard deviation and $r_{xx}$ is the reliability.
Furthermore internal consistency reliability can be calculated from the number of items $k$ and the mean inter-item correlation $\bar{r}_{ij}$ (i.e., average correlation between item $i$ and item $j$ for all $k$ items where $i\neq j$):
$$r_{xx}=\frac{k(\bar{r}_{ij})} {1 + (k -1) \bar{r}_{ij}}$$
However, I'm wanting to translate the above information into meaningful recommendations for teachers. Thus, this assumes that I have some empirical estimate of typical values of $\bar{r}_{ij}$ and that I have an estimate of $s_x$. It then requires application of the formulas to calculate standard errors of measurement for likely numbers of items $k$. In particular, I was thinking about numbers of items equal to: 10, 20, 50, 80, 100, 120, 150, and 200.
Thus, I was wondering whether there are any published estimates of the standard error of measurement teacher constructed multiple choice tests.