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Unformatted text preview: EEP 118 - midterm - answer key 6th October 2010 1 . The formula for the expectation of a linear combination of two random variables is: E ( aX + bY + c ) = aE ( X ) + bE ( Y ) + c by plugging in we get: ¯ Z = 3 ¯ X- 2 ¯ Y + 1 The formula for the variance of a linear combination of two random variables is: var ( aX + bY + c ) = a 2 var ( X ) + b 2 var ( Y ) + 2 abcov ( X,Y ) by plugging in we get: var ( Z ) = 9 var ( X ) + 4 var ( Y )- 12 cov ( X,Y ) 2 . We're asked to test for evidence that the means are di erent, so we set up the hypotheses as follows: H 0 : μ m- μ f = 0 H 0 : μ m- μ f 6 = 0 1 which means we need to do a two-tailed t-test. The t-statistic is: t = ( ¯ X m- ¯ X f )- se ( ¯ X m- ¯ X f ) The standard error of the di erence in means is: se ( ¯ X m- ¯ X f ) = s V ar ( X m ) n m + V ar ( X mf ) n f = r 200 2 100 + 320 2 64 = 44 . 72 so the t-statistic is: t = 200 44 . 72 = 4 . 47 we're not given the signi cance level, so we're free to choose one. The critical values for the 10%, 5% and 1% levels would have been 1.645, 1.960 and 2.576 respectively. Since | t | > c for all of these, we reject the null hypothesis at the 1% level (and the 5% and 10% level too). We conclude that there is statistical evidence at the 1% level that the average salary is di erent for men and women....
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- Spring '11
- Null hypothesis, $100, $2000, 0.65%, 2.15%