homework8_solutions - Math 1011 Intro to Statistics Spring...

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Math 1011– Intro to Statistics Spring 2011 HOMEWORK 8 Due Monday, 4/11/11 1. A supposedly fair coin is handed to a skeptical investigator. He flips it 731 times and obtains 397 heads. Can he conculde that the coin is biased? Solution: Null hypothesis: P ( heads ) 0 . 5. Alt hypothesis: P ( heads ) > 0 . 5. The best case for the null is P ( heads ) = 0 . 5, so assume this. Let X be the random variable counting 1 for a head, 0 for a tails in 1 flip. Then E ( X ) = 0 . 5, SE ( X ) = 0 . 5, and over the 731 flips E ( ¯ X ) = 0 . 5, SE ( ¯ X ) = 0 . 5 731 = 0 . 0185. Convert 397 731 into standard units: 397 731 - 0 . 5 0 . 0185 = 2 . 33. Then p = Area(2 . 33 , ) = 0 . 94%, so p = 0 . 0094. Thus the coin is most likely biased. 2. An investigator is attempting to breed mice that are predisposed to choose the righthand path (as opposed to the lefthand path) in a maze. He runs his current generation of mice through the maze test, and find that 40 of the 76 choose right more often than left. Has he succeeded? Solution: Null hypothesis: P ( right ) 0 . 5. Alt hypothesis: P ( right ) > 0 . 5 (i.e. more mice prefer to go right than left). The best case for the null is P ( right ) = 0 . 5, so assume this. Let X be the random variable counting 1 for a mouse preferring right, 0 for a mouse preferring left. Then
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  • Spring '11
  • DrewLewis
  • Statistics, Null hypothesis, Randomness, best case, standard units

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