{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Midterm09solutions

Midterm09solutions - EEP 118 midterm answer key 6th October...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

{[ snackBarMessage ]}

Page1 / 5

Midterm09solutions - EEP 118 midterm answer key 6th October...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon bookmark
Ask a homework question - tutors are online