Monty Hall Paradoax

Monty Hall Paradoax

 The Monty Hall Problem is how is it statisically possible that after having the ability to choose three doors, a door is eliminated with no prize, but switching from your originial choice gives you a better chance at winning the prize than staying with your originial choice. Many people believe that after one door is eliminiated that the chance of choosing the correct door is 50%. However, this is a paradoax because switching from your originial choice increases your chances by 1/3 for a total of 2/3 or 66%. Therefore, switching from your original choice gives you a better chance of winning.

 

When I played 10 times and I changed the door, I had 9 wins and 1 lose. When I played 10 times and I stayed with the door, I had 2 wins and 8 losses. This data fits with the Mythbusters data because the more you switch from your originial choice, the higher chance you have to win the game. The same goes for the more you decide to stay with your originial choice, the smaller chance you have to win the game.

When I played 1000 times and I changed the door, I had 668 wins and 332 losses. When I played 1000 times and kept the door, I had 324 wins and 676 losses. This data fits with the Mythbusters data because the more I stayed with my originial choice the less I won. I loss 676 times compared to a 324 wins. When I changed my door, I had 668 wins and 332 losses showing that I had a better chance at winning when I switched my door.

 

 Final Thoughts:

I thought the Monty Hall Problem was really interesting because when I was first watching Mythbusters I believed the same like many other people that after the first door is eliminated, your chances of winning are 50%. However, I am surprised that many people who went on Monty Hall's game show didn't do previous research to understand that switching doors gives you a 66% chance of winning. I believe that people keep their first choice because its their gut instinct and people tend not to distrust their instinct. Other game shows that would be interesting to analzye is Deal or No Deal and the chance of winning a briefcase of a $1,000,000.

 

Monty Hall-Let's Make A Deal Game Show Host

 



Empirical Rule

Empirical Rule

The Empirical Rule is also known as the 68-95-99.7 rule. This rule is used to state the distribution of data that can fall under three different standard deviations. If you break the rule down, the chance of something occuring can happen in the first standard deviation of 68%, then within two standard deviations there is a 95% chance, and lastly, within three standard deviations there is a 99.7% chance of something occuring.

An example of the using the Empirical Rule is test scores from our stats class. You can find the mean of these test scores and find the standard deviation of the test scores. Using this data, you can find the percentage of certain scores scored on the test. For example, you can find the percentage of students that scored between a 75% to an 100% on the test.

The graph would be a bell shaped curve and would look something like this...



2.1 Games Project

2.1 Games Project

For this project, Mr. May's third bell class played three different games, Bashing Pumpkins, Simon Says, and Snap Shotz, and recorded the final scores of Bashing Pumpkins and Simon Says. We recorded the highest score of Snap Shotz and each member of the class recorded their favorite game. For each set of data, I created a frequency table and different graphs for each data set. 

According to the Favorite Game Bar Graph, the most popular game in the class was Bashing Pumpkins because it had the most frequent number of students that nominated this as their favorite game. This statement would be considered inferential statistics because I made this conclusion by observing the data. 

Gummy Bear Launching

In this experiment we are trying to see whether there is a difference between launching the gummy bear on his back or on his bottom. In this experiment we used two factors the bear sitting on his bottom or the bear lying on his back. The level for this factor would be the bear sitting on his bottom and the bear lying on his back. For the second factor, we chose whether the chair worked better or without the chair. The level for this factor would be launching with the chair and launching without the chair. The four treatments that we came up with for our experiment were the bear sitting on his bottom with the chair, the bear sitting on his bottom without the chair, the bear lying on his back with the chair, and the bear lying on his back without the chair. When we tested which of the treatments worked better we had one person randomly pick from the four treatments, not knowing what order they went in on the sheet and started with that one and went through them all after that.

For collecting our data we had Alex stand in the same spot every time and he and only he shot the gummy bear. We counted by the number of tiles in the hallway and we used the tile that the bear stopped rolling or bouncing at. We had one person doing all of the counting so it was never a different method. Then once we got that number, we recorded it on our data table. Our data table was labeled with bottom with chair, bottom without chair, back with chair, and back without chair, and included 30 rounds, although we only got to 15 rounds per treatment.

Bottom With Chair Bottom Without Chair
Mean: 28.47 Mean: 62.20
Median: 24.00 Median: 63.00
Range: 57.00 Range: 126.00
Minimum: 1.00 Minimum: 3.00
Maximum: 58.00 Maximum: 129.00

Back With Chair Back Without Chair
Mean: 22.40 Mean: 40.13
Median: 24.00 Median: 34.00
Range: 36.00 Range: 108.00
Minimum: 4.00 Minimum: 13.00
Maximum: 40.00 Maximum: 121.00

We have concluded that the gummy bear went the furthest when it wasn’t using the chair. The gummy bear didn’t travel as far with the chair, this may be because it was really hard to situate the chair in the rubber band with the gummy bear sitting the right way and then shoot it the way it was supposed to be shot. We have also concluded that the gummy bear went further when it was sitting on its bottom rather than lying on its back. We think this may be because it was easier to hold and shoot if the gummy bear was vertical.

Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3

bottom w/chair 15 0 28.47 5.06 19.61 1.00 12.00 24.00 48.00

bottom w/o chair 15 0 62.20 8.43 32.64 3.00 42.00 63.00 85.00

back w/chair 15 0 22.40 2.95 11.43 4.00 9.00 24.00 31.00

back w/ochair 15 0 40.13 7.59 29.41 13.00 17.00 34.00 57.00

Variable Maximum

bottom w/chair 58.00

bottom w/o chair 129.00

back w/chair 40.00

back w/ochair 121.00

Video of Gummy Bear Launch!

Vocabulary

Vocabulary and Examples

Data vs. Statistics

Data is the numbers, measurements, observations that you collect while statistics is what you do with the data by interpreting or organizing it. For example, I record how many people buy pizza from the school which is data. The statistics is when I interpret the data to figure out how many people ordered cheese or pepperoni pizza.

Population vs. Sample

Sample is the subset of the population which is all of the outcomes or responses. For example, the people that live in Mason are the subset of the population of Ohio.

Parameters vs. Statistic

Parameter is a numerical description of a population while a statistic is a numerical description of a sample. For example, there are 850 people in the class of 2013 which is a parameter. However, there are 26 seniors in an English IV class which is a sample of the population making it a statistic.

Descriptive Statistics vs. Inferential Statistics

In descriptive statistics, you will use charts, data, and graphs to organize data. In inferential statistics, you use the charts, data, and graphs to draw conclusions. For example, if I create a line graph comparing how tall a plant grew with and without sunlight for over a year this would be a descriptive statistic. However, if I drew a conclusion that the plant grows well in sunlight then I have an inferential statistic.  

Qualitative Data vs. Quantitative Data

Qualitative data describes the qualities of something and quantitative data describes the numerical aspects of something. For example, qualitative data includes shape and texture while quantitative data is measurements.

Census- Official count of a survey or population. For example, the census of MHS would be 3,500 students. 

Survival Activity

Survival Activity

1. The activity I completed over the last two days was that we were given 11 items and we had to rank them    1-11 in order of importance in a survival situation. Then, we went into separate groups and discussed group rankings which we compared with the rest of the class. We used the class group rankings as data and found the mean, median, and range of the data. Our group used the data and discussed the items that were ranked the same by every group, ranked differently by every group, and used statistics to justify our answers. Then, we were told an expert's rank and we found the absolute difference between the expert and our personal rank. Our class discovered in the end that the closer your absolute value difference was to zero the better your personal ranks were was to the expert's opinion. 

2. Our group was pretty average in how well we would have survived. Our group's average for our absolute value difference was 2.54. I did this by using our group ranks and taking the absolute value difference of those ranks compared to the expert's rank. I believe that is average compared to the expert's average absolute difference of zero. The closer your absolute value difference is to zero, the better your group would have survived.

3. As an individual, I believe I was pretty average in how I survived. My average absolute value difference was 2.72. I did better with my group than I did as an individual but I believe that my average was higher because I ranked the cigarette lighter as 11, while the expert ranked it 1. The bigger the absolute differences were between my personal rank and the expert rank made my average higher like the small ax.