Zenar cards were developed in the 1930s to test people for ExtraSensory Percepti

Question

Zenar cards were developed in the 1930s to test people for ExtraSensory Perception (ESP). A set of Zenar cards consists of fivecards each marked with one of the following symbols:

CIRCLE, CROSS, WAVY LINES, SQUARE and STAR

A group of researchers designed a test in which one of the 5 Zenarcards was randomly selected and placed face down in front of aself-described psychic. The psychic then tried to identify which ofthe 5 symbols was on the face of the card. 40 trials wereperformed, and the number of successful trials (correctlyidentified cards) were counted.

The research hypothesis was: "The psychic has the ability toidentify cards with greater probability than random guessing."

- What are the null hypothesis and research hypothesis writtensymbolically?

- With a level of significance of 0.05, what is the minimum numberof successful trials needed to reject the null hypothesis?

- The psychic managed to produce 11 successful trials. What is thep-value associated with this result?

Explanation / Answer

The Null Hypothesis is =8; The psychic's succesfulselection of the correct card is no better than random guessing(1/5 of 40 is 8). Alternate Hypothesis: is greater than 8; the physchissuccesful selection of the correct card is significantly betterthan random guess. Part b) The probability of getting a number of at least xnumber of successes is given by 1-binomcdf(40,1/5,x). Solving thisequation for .05 or less, using trial and error, we get x=12,(binomcdf(40,1/5,12)˜.04324) So, the mimnum number of trialsneeded is 12. Part c) Because the fortune teller only got 11 trials correct,the p-value is .0875, or about 8.75%.

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