So now we want to use the coin tosses to model the "just guessing" choices people make between the two faces. Using coin tosses is valid because we are assuming each and every person was equally likely to put Tim on the left (=Heads) or Bob (=Tails).
(d) In the applet below, you want to keep the probability of heads set to .5. Why?
(e) What do you need to change the number of tosses to? Why?
Below is an internet applet you are to use for this lab. Underneath the applet are instructions on how to use the applet. If you get really stuck, there is an interactive demo version here. If applet doesn't display in window, try here.
An alternative version of the applet that works on the iPad but not in IE can be found here.
Generate a "could have been" outcome (to see what could have happened if everyone had just flipped a coin to make their choice):
- (Set the Number of tosses)
- Press the Toss Coins button. Note the number of heads. [Note: The animation here does not current work on a Mac, there will just be a long pause.]
- Click in the circle next to Proportion of heads. This will rescale the x-axis. Note (and verify) the proportion of heads for this first repetition.
- Click the Toss Coins button again. The new value is added to the graph in blue.
(f) How many heads did you get in your first repetition? What proportion of heads did you get in your first repetition? If we repeat this process many more times, will we always get this same proportion of heads? Explain.
- Now change the Number of repetitions from 1 to 10, and click Toss Coins. Be sure to watch the animation. (Note: This animation only appears on PCs right now, on Macs there will just be a pause.)
Notice that the results are being graphed in a "dotplot" because we have a quantitative variable.
(g) What are the observational units and variable in this dotplot? [Hints: Call this the "null distribution." You should give different answers from question (a)! What do you have to do to add another dot to the dotplot? This is your observational unit...]
The previous question is pretty important, ask the instructor or TA if you are not sure.