First, answer this intuitive problem

Suppose that I place a $100 bill in one of three envelopes, which are labeled A, B, and C. You are told that if you can correctly guess which envelope contains the $100 bill, you can keep it. You can’t see the bill through the envelope, so you are entirely guessing. Let’s say that you say it’s in the envelope marked B. You are told that it’s definitely not in the envelope marked C, and I offer to let you switch to envelope A, or to stay with envelope B. (Assume that I am telling the truth, that the bill is indeed not in envelope C.) What should you do? Stay or switch? What would be your rationale for doing what you decide to do?

Second, collect some data

Set up your own version of this demonstration as an experiment. Make 5 copies of the chart, PSY101_Wk1_Chart, to record your results. After completing your results and forming your conclusion, be sure to include the charts as an attachment with your response. You will find that this chart includes: Correct answer, Participant’s choice, Stay/Switch, Win/Lose. 

Decide in advance which letter will be the correct choice for each of the 10 trials: A, B, or C. List the correct answer under the column heading “correct answer,” and make sure that your subject can’t see your list. 

Select five friends/family members to serve as your subjects. You will test each subject away from any other potential subjects. 

Tell your subject that he or she is to guess which letter you are thinking of on each trial. When the subject makes his or her guess, write it down under the column heading “Participant’s choice.” Then, tell the subject which letter is definitely notthe correct answer (always eliminate something other than the letter the subject has chosen and, of course, don’t eliminate the correct answer). If he or she has chosen the correct letter, that’s okay! Just eliminate one of the other two letters. Then ask the subject if he or she wants to stay with the letter he or she chose, or switch to the other letter. Record under the “Stay/Switch” column whether the subject decided to stay with his or her original choice or switch to the other option. Next, record whether the subject was right or wrong under the “Win/Lose” heading. Don’t tell your subject what the correct answer was if he or she loses because he or she will be looking for your “random” pattern. Just say “win” or “lose” and ask for his or her next guess. 

Once you have collected data from all 5 subjects, tally up the percentage of wins when the subjects stayed and the percentage of wins when they switched. To do that, count up how many times each subject stayed, and use that as the denominator. (You’ll be collapsing the data for all five subjects together, so count how many times, all together, they stayed.) Then, count up how many times the subjects won when they stayed and use that as the numerator. So, if your subjects stayed a total of 20 times and won a total of 5 times when they stayed, you would find that staying led to 5/20 wins or 25% of the time they won when they stayed. 

Do the same procedure for switches. Count up how many times they switched and use that number as the denominator, then count up how many times they won when they switched, and divide. Compare the percentages for the wins when they stayed versus the wins when they switched.What do the results of the experiment reflect?Do these percentages conform to your rationale that you provided earlier?Does this demonstration make a case for the need for collecting data in psychology, rather than relying on our intuition? Explain your answers and incorporate your data results into your conclusion.Write a summary discussing the importance of emperical research.Include your charts (data collection) as an appendix at the end of your paper.