MAGIC 8-BALL

1. MAGIC 8-BALL By: Connie Saltzman, Brandi Kaminski, & Joe Muller

2. The Facts • The Magic 8 Ball has been used for fortune telling since its creation by Tyco in 1946. • It is a hollow, plastic sphere resembling an oversized, black and white 8-ball. • The fortunes are given by a white plastic die in the shape of an icosahedron, floating in a blue liquid, with answers to yes-no questions in raised letters on its 20 triangular faces.

3. MAGIC!!! • We shook the 8-ball 80 times in the same two-hand manner to increase accuracy of our experiment and destroy lurking variables LURKING VARIABLES This is really how 8-balls are made. Not in a factory, but by wizards.

4. Does our frequency distribution of responses match that of the expected distribution of eight ball responses?

5. 50%-YES 25%-AMBIGUOUS 25%-NO • Signs point to yes. • Yes. • Most likely. • Without a doubt. • Yes – definitely. • As I see it, yes. • You may rely on it. • Outlook good. • It is certain. • It is decidedly so. • Reply hazy, try again. • Better not tell you now. • Ask again later. • Concentrate and ask again. • Cannot predict now. • My sources say no. • Very doubtful. • My reply is no. • Outlook not so good. • Don't count on it. Expected Responses

6. After a series of 80 trials we found our responses to be close to the expected. • The graph below is a comparison of our data to the expected.

7. 45% 50% 25% 31% 25% 24% • The “no” response had the largest difference in % between observed and expected. Ambiguous had very similar frequencies, and “yes” was in the middle. In general, the expected and observed responses were similar.

8. Chi-Squared Goodness of Fit Test Assumptions • SRS • Sample size is large enough that all expected counts > 5

9. Chi-Squared Goodness of Fit Test • Ho: the observed distribution of magic 8-ball responses fits that of the expected distribution • Ha: the observed distribution of magic 8-ball responses does not fit that of the expected distribution • Test Statistic: • ² = (obs-exp) ² = (.45-.5) ² + (.2375-.25) ² + (.3125-.25) ² = 1.7 exp .5 .25 .25 P-value = P(² > 1.7) = tcdf(1.7, E99, 2) = .1156 df = 2

10. Conclusions We fail to reject our Ho in favor of our Ha because our p-value is >  = .05. We have sufficient evidence that the observed distribution of magic 8-ball responses fits our expected distribution.

11. Bias/Error • Answers sometimes got stuck, eliminating that shake • Bubbles blurred responses, and additional shakes were needed • Because of human error, shakes could not be exactly alike each time A magic 8-ball error has occurred. Do you wish to continue?

12. Application? So many people put their lives in the hands of the magic 8-ball. We had to test its claimed answers for the good of humanity.

13. Personal Opinions/Conclusions • We expected our experimental conclusions to be very similar to that of the expected. Because we found the standard distribution of answers, and we used standard 8-balls, and we had a high n, there was no evident reason the distributions would not match. • Magic 8-balls are very fun, but through our experiment we have come to the conclusion that they should not be believed and followed at all costs. The reason for this is that they are manufactured in factories, not by wizards, and they do not accurately signify one’s fate.

14. Class Activity www.bobainsworth.com/games/games.htm • Shake the ball ONCE and remember your response. • Raise your hand when I call it. Does the class's distribution fit the expected? Does the online version make a difference?