Question

PROJECT B

1. Flip a coin 120 times. In order to be organized, please record the results of this experiment in 5 rows, with 24 flips per row. For example, the first row may be

HTHTTTHTTHTTHHHTTHTHHHHT

If you do not desire to flip a coin manually, STATDISK can be used to simulate the process. To use STATDISK, go to “Data” at the top of the STATDISK window, and then choose “Coins Generator”. The “Coin Toss Simulator” window will appear. Then in that window, put 120 in for “Sample Size” and put 1 in for “Num Coins”. Please disregard the “Random Seed” textbox. Then, click “Generate”.

Then, on the right side of the window you will see a set of 0’s and 1’s

which are the results of each toss of the die. We can let 1 represent “H” and 0 represent “T”. In the meantime, let the 0’s and 1’s be Data Set A.

2. For each pair of flips, write down the number of heads in that pair. For the 24 flips shown above, this would be done as follows:

PAIR NUMBER OF HEADS

HT1 HT1 TT0 HT1 TH1 TT0 HH2 HT1 TH1 TH1 HH2 HT1

Note that the result will be a data set with 60 numbers such that each number is either 0, 1, or 2. Take each of those 60 numbers and divide by 2. To make it easier, please feel free to use Microsoft Excel or STATDISK. For STATDISK, go to the “Coin Toss Simulator” window and click “Copy”. Then, go to the “Statdisk Data Window” and click “Paste”. Please select a column to paste into. For simplicity, let’s choose Column 1. Then, go to the top and click “Data” and choose “Sample Transformations”. The “Sample Transformer” window will appear. Into this window, enter the Source column (in this case, 1), for the operation, and enter “/” because you want to divide. Then, choose “Constant”. Also, enter in 2 into the field next to “Constant”. Click the “Basic Transform” button, and you get a new data set obtained by dividing each number in the former data set by 2. Now, take those new numbers and refer to these numbers as Data Set B.

3. Repeat #2 above except for each triple of flips. For the 24 flips shown above, the result would be

TRIPLE NUMBER OF HEADS

HTH 2 TTT 0 HTT 1 HTT 1 HHH 3 TTH 1 THH 2 HHT 2

The full data set will have 40 numbers such that each number is either 0, 1, 2, or 3. Divide each of these 40 numbers by 3. Refer to this new data set as Data Set C.

4. For Data Set A, make a frequency distribution with class width of 1 and having 2

classes. This frequency distribution will display how often each of the two numbers in your data came up.

5. For Data Set B, make a frequency distribution with class width of 1/2 and having 3 classes. This frequency distribution will display how often each of the three numbers in your data came up.

6. For Data Set C, make a frequency distribution with class width of 1/3 (not .3 or

even .33, but 1/3 exactly ) and having 4 classes. This frequency distribution will display how often each of the four numbers in your data came up.

7. Using these frequency distributions, draw relative frequency histograms for each of Data Sets A, B, and C and using each histogram, please describe what the distribution of each of the data sets is. NOTE: A relative frequency distribution is is the same as a probability distribution, so the y-axis of a relative frequency histogram has probabilities or percentages.

8.Without doing any calculations, draw a rough picture of what you think the relative-frequency histogram for groups of four flips may look like. Briefly justify your picture.

For Data Sets A, B, and C, compute the mean and standard deviation. Please describe any comparisons or contrasts that you see among the 3 sets of means and standard deviations.

Answer 1