Please read the entire assignment. What you're supposed to submit is at the end.

The overall plan of this assignment is to take two random samples from a group of 800 students and compare them.

Assume that at a certain college there are 800 students, 200 of which are over the age of 30 (and therefore 600 of the students are thirty years old or younger). We are going to take two random samples from the student body, one of size 8 and one of size 16. Each sample will give us an estimate of the fraction of the students who are over the age of 30. We are going to compare the two estimates.

The Details: Assume that you have labeled the students with the numbers 1 through 800 with the 200 students who are over the age of 30 labeled with the numbers 1 through 200 and the 600 students 30 years of age and under labeled with the numbers 201 through 800. Do the following:

1. Choose a random sample of size 8 by generating 8 random numbers (or more if you get some repeats) between 1 and 800. The easy way to is to use the random number generator at https://www.calculatorsoup.com/calculators/statistics/random-number-generator.php(Links to an external site.)
2. Use the random numbers to choose a sample of size 8 and find the fraction of the sample consisting of people over 30 years of age. (So, for example, if one of your random numbers was 223 then the person numbered 223 would be in your sample. All you would know about this person is that the person is 30 years of age or under since his/her number falls in the range 201 through 800.)
3. Repeat steps 1 and 2 but this time choose a random sample of size 16.
4. Calculate the probability that in a sample of size 16 the fraction of the sample consisting of students over 30 years of age is between 1/8 and 3/8. Note that the same probability for a sample of size 8 is calculated on the video for this module.

What you should include in what you submit: (You can either type in your answer on Canvas or upload a file.)

Tell me the method you used to get your random numbers and list the 8 random numbers for the first sample and the 16 random numbers you got for the second sample. For both samples give the fraction of the sample of students over 30 years of age. This number can be a fraction, decimal or percent, whichever you prefer. Show me your calculations for the probability that in the sample of size 16 the sample percentage is between 1/8 and 3/8. Please use complete sentences so I can tell what is what. Then answer the following questions (in complete sentences):

• Which sample (size 8 or size 16) gives a better representation of the population?
• Do you think this is a coincidence or an instance of some general principle? (Your opinion.)
• Which of the following two procedures do you think would give a better estimate of the entire population fraction of students over 30? (Or do you think they would give equally good estimates?)
  1. Increase the sample size to 50 and find the fraction of students over 30 in this sample.
  2. Take five samples of size 10, find the fraction of students over 30 in each sample and take the average of these five numbers (by adding them and then dividing by 5.)