Simulate Probability Data

Description

This applet is based on a scenario from a popular game show from the 1960s. Contestants are asked to choose one of three doors. Behind one is a fabulous prize! Behind the others are gag gifts. When a contestant chooses a door, the game show host shows the contestant a gag gift behind one of the two doors that were not chosen. The contestant is then given the option of switching to the one remaining door that has not been opened or staying with their original choice.

This applet allows users to play the game repeatedly to determine what is the best strategy for winning the prize. Doors are chosen by clicking on the numbers one through three. The user starts a game by selecting a door. The door the user selects will be outlined. One door with a gag gift (represented by a donkey) is then revealed. The user has the choice to either stay with their original door by clicking on it again, or to switch to the remaining closed door by clicking on it. After the user has made their decision, the location of the prize is revealed. A new game can be started by clicking on any door.
The table at the bottom of the game area keeps track of the total wins and losses with each strategy. The raw results from the games from this applet can be added to the StatCrunch data table by clicking the Analyze button.

Instructions

Part I: I Have Attached my Results/ Data after playing the game

Conduct this activity in MyLab by Pearson

Opening and playing the game:

Select “Content” from the Brightspace navigation menu.
Select “MyLab Statistics” tab from the “Content” menu.
Click on the “MTH 210 StatCrunch” tab
Click on “Open Link”
Go to the second arrow: Click on Visit the StatCrunch Website
Click on the Orange > Open StatCrunch
Click on Applets > Games > Let’s Make a Deal
A new window will pop up with 3 different doors to choose from. Click on one of the numbers to start the game. One door with a gag gift (represented by a donkey) is then revealed. You can now either choose to stay with your original door by clicking on it again, or to switch to the remaining closed door by clicking on it. After you have made your decision, the location of the prize is revealed. A new game can be started by clicking on any door (do not press reset unless you want to start over again- all your data will be removed).

Data simulation and comparison :

Stay with your original door choice 5 times and then choose another door 5 times. Which strategy was more effective in this small sample size? Is there a significant difference in the results based on what you simulated?

Continue to play the game as many times as you want to get a large sample size (50 times playing the game is recommended).

Click on Analyze and your data will be placed into two columns “Result” and “Strategy”.

Generate a table and graph your results:

Click on Stat > Tables > Frequency

Select Column “Strategy” and Group by “Result” and select for Statistic (s) “Percent of Total”, then hit Compute!

A table will be generated. Copy and paste into to a word document.

Next, click on Graph > Bar Plot > With Data

Select Column “Strategy” and Group by “Result”, and select for Type “Percent”, then hit “Compute!”

A graph will be generated. Copy and paste into a word document.

Part II:

Answer the following questions in the submission box

Analysis:

From your table and your graph, what conclusions can you draw when comparing the strategies for switching versus staying? Is there clearly a better strategy when playing this game?

What would be an important next step as a statistician to ensure your conclusions about the best game strategy is correct? How do we know that with this simulation, it wasn’t just by chance to get such a big difference between switching versus staying?