Reference no: EM13132644
In this part of the project you will investigate sampling distributions and model for proportion of heads that may show up when a coin is tossed repeatedly. Toss the coins if you want, but it's much easier to do a simulation with a calculator. One way to do this is to generate 0's and 1's with equal probability, with 1 representing heads. By adding up all the 1's you can effectively count the number of heads. Dividing that count by the number of tosses will result in , the sample proportion of heads.
On the TI 83 / 84 you can use the randInt command to randomly generate 0's or 1's:
1. select the "MATH" key,
2. arrow to the right to "PRB",
3. arrow key down to "5:randInt("
4. select "enter" ("randInt(" should be on the main screen)
5. enter "0,1)"
6. select "enter" (the output will randomly be either 0 or 1)
Selecting "enter" again and again will randomly output either 0 or 1. If you want the calculator to select ten random 0's or 1's in a row on step 5 above enter "0, 1, 10)". You will need to use the left and right arrow keys to view all of the 10 randomly selected 0's and 1's. By adding up all the 1's you can effectively count the number of heads. Dividing that count by the number of tosses will result in , the sample proportion of heads.
1) Set up a calculator or computer's random number generator to simulate flipping a coin 10 times.
2) Run 50 trials, recording all the sample proportions and make a relative frequency histogram of the results.
3) Repeat your simulation, this time tossing the coin 20 times. Again make a histogram of the 50 sample
proportions.
4) Compare the two distributions of the proportions of heads observed in your simulations from part 1 and 2.
5) Describe the theoretical sampling distribution model for 20 tosses.
6) Compare the mean and standard deviation of the actual distribution of your 50 sample proportions for 20 tosses to what the theoretical sampling distribution model says the mean and standard deviation should be.
7) Describe how your results might differ if you had run 50 tosses and 50 trials.
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