To test whether my friend\'s sh Googly had psychic powers, I wrote R code to dis

Question

To test whether my friend's sh Googly had psychic powers, I wrote R code to display two windows. I entered either Left" or Right" depending on which way Googly was facing. Then the random number generator in R selected either the left or the right window, with probability 0.5 for each, in which to display a star. Let p be the probability Googly guesses correctly on a given trial (assume this is constant.) In 80 trials, Googly correctly guessed the window with the star 41 times. 1. Using mathematical notation, write down null and alternative hypotheses for a one-sided test. 2. If the test statistic is the number of correct guesses (41) in 80 trials, write down R code to nd the P-value of a one-sided test. 3. Even without R, we can see that Googly's success rate was close to its expected value under the null, so the one-tailed P-value will be close to 0.5. State your conclusion about the she's psychic powers. 4. Continued from part (b). If you only knon that the R code dbinom(40, 80, 0.5) gives the number 0.0889, how would you nd the exact P-value of the test?

Explanation / Answer

If, at any time, you want to stop, press STOP. The test lasts roughly a minute and half (102 seconds). After you started, try to influence how many times the computer generate the number 1: focus on the number 1, or visualize the green bar going further to the right (whatever seems to work best). The green bar shows how many more time the number 1 has been generated compared to the number 0 (vice versa for the red bar). The little triangles underneath indicate the best score (difference of a number over another) you have reached during the test. A normal result close to 50% for each number would display very little bars in the middle.

The goal is to push the bar close to the right or left edge, so that the number of times one number has been generated is statistically improbable. If you reach the edge, you either possess telekinetic abilities or your computer experienced a serious fluke! Your statistics will be displayed at the bottom during the test, such as the current score, the total each number has been generated and the time remaining, but don't let it distract you too much. You can also decide to influence 0s instead of 1s (in this case, try to push the red bar to the left with your mind).Since the creation of this test, a few people have asked me more details about the mechanism so they can know where to consciously focus their efforts: It is programmed in Javascript, which means it is controlled by your browser, hence your computer, your memory and your CPU. It is not server based. If you succeed in influencing it substantially, it means you have influenced your computer... which even some scientists speculate it might be possible simply from an bio-electrical point of view. Some computers always have problems with certain individuals

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