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# 409Quiz3Eans - Decision The value of the test statistic is...

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STAT 409 Fall 2011 Version E Name ANSWERS . Quiz 3 (10 points) Be sure to show all your work; your partial credit might depend on it. No credit will be given without supporting work. 1. Last season, a baseball player’s performance was as follows: Day Games Night Games At bat, n i ( “attempts” ) 240 160 Base hits, Y i ( “successes” ) 72 56 a) (5) Test H 0 : p Day = 0.34 vs. H 1 : p Day < 0.34 at a 10% level of significance. Y = 72. n = 240. 240 72 Y ˆ = = n p = 0.30. Test Statistic: Z = ( ) 240 66 . 0 34 . 0 34 . 0 30 . 0 1 0 0 0 ˆ - = - - n p p p p = 1.31 . P-value: Left – tailed. P-value = P( Z 1.31 ) = 0.0951 . Decision: P-value < α = 0.10. Reject H 0 at α = 0.10. OR Rejection Region: Reject H 0 if Z < – z α z 0.10 = – 1.282.

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Unformatted text preview: Decision: The value of the test statistic is in the Rejection Region. Reject H at α = 0.10. b) (5) The player claims that he hits better during night games than during day games. Find the p-value of the test H : p Day = p Night vs. H 1 : p Day < p Night . 240 72 Y 1 1 1 ˆ = = n p = 0.30. 160 56 Y 2 2 2 ˆ = = n p = 0.35. 32 . ˆ 400 128 160 240 56 72 Y Y 2 1 2 1 = = + + = + + = n n p . Test Statistic: Z = +-⋅ ⋅ 160 1 240 1 68 . 32 . 35 . 30 . = – 1.05 . P-value: Left – tailed. P-value = ( area of the left tail ) = P( Z ≤ – 1.05 ) = 0.1469 ....
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409Quiz3Eans - Decision The value of the test statistic is...

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