A multiple-choice quiz contains ten (n = 10) questions. For each question there

Question

A multiple-choice quiz contains ten (n = 10) questions. For each question there is one correct answer and four incorrect answers (so choose one of a, b, c, d, or e). A student gets three correct answers on the quiz. Test the hypothesis that the student is guessing, against the alternative that his probability of a correct answer is higher than for a random guesser: H_0: p = _____ vs H_1: p ____ _____. (You need one number, and one inequality sign). P_p(B greaterthanorequalto 3] = ______ (the subscript p is your answer on the previous line, B is the number of correct answers) Suppose that if a student gets 4 or more questions correct, the hypothesis that a student is a "guesser" is rejected. What is the power of this test for a student who has the following probability for a correct answer on each question: p = A, power = P_A[B greaterthanorequalto 4] = ________; P = .5, power = _________;p = .6, power = _______

Explanation / Answer

1) Selecting a correct alternative out of 5, probability = 1/5 = 0.2

H0 : p = 0.2

Ha : p >= 0.2

p = 0.2 , q = 0.8

P(B>=3) = 1 - (10C0 *p^0 * q^10 + 10C1 *p^1 * q^9 + 10C2 *p^2 * q^8)

= 1 - (10C0 * 0.2^0 * 0.8^10 + 10C1 * 0.2^1 * 0.8^9 + 10C2 * 0.2^2 * 0.8^8)

= 1 - ( 0.6778)

= 0.3222

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