Central Limit Theorem

  

Central Limit TheoremEach week, you will be asked to respond to the prompt or prompts in the discussion forum. Your initial post should be 75-150 words in length, and is due on Sunday. By Tuesday, you should respond to two additional posts from your peers.For the last several weeks, you have been working with this scenario.ABC Enterprises is a growing company in which employees must frequently travel for business. Currently, each employee is allotted 30 dollars each day to cover all meals. Employees have complained that this is not enough, especially when traveling to some of the more costly cities and countries. A survey was taken to get recommendations for a new allotment. Although not all responded, the response rate was good.This week, we are going to use the Central Limit Theorem. We are going to pretend that our data set represents the entire population of ABC Company. It doesn’t, but we are going to pretend that it does.1. What is the mean dollar amount that is recommended by the population of employees?2. Now, we are going take 3 samples of 10 dollar amounts from the spreadsheet and average (find the mean of) them. Open the spreadsheet and make sure you are on the Week 4 tab.Go to the random number generator at https://www.google.com/search?q=random+number+generator&oq=random+number&aqs=chrome.0.0j69i57j0l6.3428j0j7&sourceid=chrome&ie=UTF-8(or any other random number generator)Put in the minimum number of 5 (this aligns with the cell that begins your list of numbers).Put in the maximum number of 56 (this aligns with the cell that ends your list of numbers).Hit “generate.”The number given tells you what cell to go to. For example, if I got a 48 on the random number generator, I would put my cursor in cell 48 and record the number that is there. For example, if there were a “75” in that cell on the Excel spreadsheet, I would write down 75. Continue to hit the random number generator 9 more times. Record the other 9 values in the cells. Do not worry about repeats. Provide your list of the 10 values from the cells.Average (find the mean of) those ten values. Write down your sample mean.Repeat this exercise two more times. You will have a total of three sample means.3. Comment on your three means of the samples. Were they the same? How did they compare to the mean of the population? Were the samples representative of the population? Why or why not?4. If you took your 3 sample means and gathered the 3 sample means from all your classmates and put them on a histogram, what should the shape of that histogram be? Why? How does this relate to the Central Limit Theorem?

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