In order to determine whether you have ESP (extrasensory perception), you are shown the back of a card and asked to guess whether it has a 1, 2, 3, or 4 on the front. The card is selected at random from four cards numbered 1, 2, 3, and 4. This is repeated 100 times, and the number of correct guesses you make is recorded. a. Describe the shape, mean, and standard error of the sampling distribution of the number of correct guesses if you do not have ESP. b. What is the probability that you guess right 30 or more times? c. If a person guesses right 35 times, what would you conclude?
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Since there are 4 cards and you are guessing randomly, the probability of guessing the correct card is $\frac{1}{4}$, and the probability of guessing incorrectly is $\frac{3}{4}$. Show more…
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One extrasensory perception (ESP) test asks the subject to view the backs of cards and identify whether a circle, square, star, or cross is on the front of each card. If $p$ is the proportion of correct answers, this may be viewed as a hypothesis test with $H_{0}: p=0.25$ and $H_{a}: p>0.25 .$ The subject is recognized to have ESP when the null hypothesis is rejected. What would a Type II error result in? (A) Correctly recognizing someone has ESP (B) Mistakenly thinking someone has ESP (C) Not recognizing that someone really has ESP (D) Correctly realizing that someone doesn't have ESP (E) Failing to understand the nature of ESP
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An extrasensory perception (ESP) experiment is conducted by a psychologist. For part of the experiment, the psychologist takes 10 cards numbered $1-10$ and shuffles them. Then she looks at the cards one at a time. While she looks at each card, the subject writes down the number he thinks is on the card. a. How many possibilities are there for the order in which the subject writes down the numbers? b. If the subject has no ESP and is just guessing each time, what is the probability that he writes down the numbers in the correct order, that is, in the order that the cards are actually arranged? c. Based on your result from part (b), what would you conclude if the subject writes down the numbers in the correct order? Explain your answer.
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