Discussion Question 1: Central Limit Theorem The Central Limit Theorem and its role in shaping the sampling distributions is one of the most funda mental concepts of statistics and one of the most difcult to communicate through text alone. Khan's videos do a great job of bringing these concepts to light using drawings and animations. This discussion question is not a specic question but I want it to be a freeowing discussion of the Central Limit Theorem and the Sampling Distributions. View the following Khan Academy videos and comment on them or ask questions regarding them. They are each approximately 10 minutes in length (clickable links}: (1} Central Limit Theorem. (2} The Sampling Distribution of the Sample Mean. (3} The Sampling Distribution of the Sample Mean 2. One quibble I have with Khan's videos is that he is sometimes sloppy with technical terms. Be warned that in these videos he uses the word \"sample\" in two different ways. When you take a group of ve subjects from a population and measure the mean of some variable, that is one sample. Khan sometimes refers to the ve subjects as \"samples.\" This is not correct. The ve subjects make up one sample. Watch these videos with a critical eye and ask questions if there is something you do not understand or if you think you have caught an error. Here is the link of the App that Khan used in the The Sampling Distribution of the Sample Mean. http:[/onlinestatbook.com/stat.sim/sampling.dist/index.html In this discussion question, we will replicate what Khan did with your data set found in Week 2. Make sure your data set has at least 100 cases. (Note: Ifyour data set is extremely skewed, you will need at least 200 cases in your data set to get the desired result.) (1} Pick a quantitative data and use Statkey to sketch a histogram. If the distribution looks approxi mately normal, choose a different one and make sure that it is nonnormal, e.g. left or right skewed (the more nonnormal, the better}. You may have already done this for Week 2. Feel free to reuse the histogram. (2} Now use the sampling distribution for a mean in Statkey. Pick the sample size to be H = 2 and generate 1000 samples. Describe the shape of the distribution and upload a picture of it. (3} Change 71 = 8, generate 1000 samples. Describe the shape of the distribution and upload a picture of it. (4} Change it = 32, generate 1000 samples. Describe the shape of the distribution and upload a picture of it. 1 2 ACTIVITIES AND ASSIGNMENTS FOR WEEK 5 (5} What changes and non-changes have you noticed about the distribution (e.g. shape, mean, standard error, etc}