Lab 3 Instructions-2

MATH 15 - LAB 3 (Excel 2016)

The Central Limit Theorem

Consider a binomial distribution with n = 10 and p = 0.1.

Questions 1, 2, and 3 are theoretical; calculate the answers using the information from lecture.  For 3, please note the title of this lab!  You will compare the theoretical answers to your experimental answers generated from your 500 random samples of size 35, of 10 trials.

I highly recommend that you do this lab in a group. Spreading the work out among multiple people will be a big time saver.

Create a document with the histogram of your 500 sample means in either .pdf, .doc, or .docx format.  In the Lab 3 Answers. You may use the File Lab 3 Answers File.docx Download Lab 3 Answers File.docx to upload into the assignment:

 

  1. Consider a binomial distribution with n=10 and p=0.1. (Remember that N=10 refers to the number of trials in a single binomial experiment where p is the probability of success in each trial.)  Using the terminology from class, how would you describe the shape of this binomial distribution?
  2. Consider the same binomial distribution. Calculate the mean and the standard deviation of this binomial distribution.
  3. Consider a sample of size n=35 from the same binomial distribution. (This means that you do the previously mentioned binomial experiment 35 times, the binomial experiment will still have 10 trials. So, this is a ten trial experiment done 35 times.)   What does the Central Limit Theorem tell you about the sampling distribution of \overline{x} ¯x?  Include the population mean and standard deviation of the sampling distribution, as well as a description of the shape of the distribution in your answer.

  4. Use Excel to run your simulation and generate 500 sample means where your sample size is n = 35, from the binomial experiment where the number of trials is N = 10, the mean and standard deviation of the sample means, and the histogram. (see the Simulation Instructions)

  5. Calculate the mean and standard deviation of the 500 sample means.  Instructions for this can also be found in the Simulation Instructions.

  6. Compare the shape of your histogram in 5 to your answer to problem 3, are they the same or different?  Did you expect this answer?  Why?

  7. Compare the mean and standard deviation in problem 3 with the values you got from 5 above.  Are they similar?  Should they be?

  8. Do your findings from problems 6 and 7 support your answer to problem 3?