A simulation study was used to show the relationship between the STANDARD ERROR ON THE MEAN (SEM) and the sample size. However, that simulation used random.random() to generate the random values. You must perform a similar simulation to study the relationship between the SEM and sample size associated with the random.gauss() function. You must use all skills up to this point in lecture to program the SEM simulation. This problem is more open ended than the previous ones. Previous problems in this assignment required you to define functions that are important to this simulation. You therefore have most of the pieces necessary for the simulation! There are a few steps that still need to be created though. Also, certain aspects of the solution are provided to you since we have not discussed visualization yet. You must generate all random values using a mean of 100 and standard deviation of 25. You must replicate calculating the sample average 5000 times when calculating the standard error on the mean for a given sample size. You must visualize the SEM with respect to the sample size on a plot similar to the one created in the lecture example. The specific sample sizes you must use are provided in the cell below.

In[]:sample_size_use = [5, 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10240]