HW8 - Solution to HW8 Problem 1 2 1 2 1 μ μ μ μ ≠ ↔...

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Unformatted text preview: Solution to HW8: Problem 1: 2 1 2 1 : : μ μ μ μ ≠ ↔ = a H H n X X n i i ∑ = = 1 and ) 1 ( ) ( 2 1 2 − − = ∑ = n X X s n i i Male: 57143 . 69 , 7 1 1 = = X n and 7.285714 2 1 = s Female: 5 . 64 , 8 2 2 = = X n and 13.14286 2 2 = s Pooled t-test statistic: 10.43956 2 8 7 14286 . 13 7 285714 . 7 6 2 ) 1 ( ) 1 ( 2 1 2 2 2 2 1 1 2 = − + × + × = − + − + − = n n s n s n s p 3.032757 ) 8 / 1 7 / 1 ( 44 . 10 5 . 64 57143 . 69 1 1 2 1 2 1 = + × − = + − = n n s X X T p with 13 = df From the t-table, the p-value is between 0.0025 and 0.005 for one sided test. In this problem, it is a two-sided test, so 01 . 005 . < − < value p . Unpooled t-test statistic: 3.095747 8 / 14286 . 13 7 / 285714 . 7 5 . 64 57143 . 69 2 2 2 1 2 1 2 1 = + − = + − = ∗ n s n s X X T 12 12.72191 7 ) 8 / 143 . 713 ( 6 ) 7 / 286 . 7 ( 8 143 . 13 7 286 . 7 1 ) / ( 1 ) / ( 2 2 2 2 2 2 2 1 2 1 2 1 2 2 2 2 1 2 1 ≈ = + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + = − + − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + = n n s n n s n s n s ν Again the p-value is between 0.005 and 0.01 for a two-sided test....
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HW8 - Solution to HW8 Problem 1 2 1 2 1 μ μ μ μ ≠ ↔...

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