s07pre1a

# s07pre1a - Prof G Jakubson Economics 321 Spring 2007...

This preview shows pages 1–2. Sign up to view the full content.

Prof. G. Jakubson Economics 321 Spring 2007 PRELIMINARY EXAM #1 - ANSWER KEY 1. Class intervals for infant mortality rate Countries cum rel freq rel freq freq 0 to <10 24 24/131 = .18 24/131 = .18 10 to < 20 24 24/131 = .18 48/131 = .36 20 to <30 14 14/131 = .11 62/131 = .47 30 to <50 18 18/131 = .14 80/131 = .61 50 to <75 18 18/131 = .14 98/131 = .75 75 to <100 16 16/131 = .12 114/131 = .87 100 to <140 13 13/131 = .10 127/131 = .97 140 to 180 4 4/131 = .03 131/131 = 1 Total number of countries 131 a. Median infant mortality rate is in the 30 to < 50 category. Since we were asked for the median and not just the class, we must interpolate: Median = 30 + [.5 - .47)/.14]*(50-30) = 34.3. This assumes a uniform distribution within the class. b. See above. c. Use grouped mean and variance expressions: Mean = xf x n n k k k k k k ∑∑ = and Variance = n n xx f k k k 1 2 () , where x k is the class mark and f k is relative frequency. 2. a. [] Z= 1 n ∑− =∑ −∑=−= XX s n X sn X s X s X s ix i x x / 11 0 or use the linear transformation formulae: Z i = a + bX i where x x s 1 b and s X - a = = b. s z = (1/s x ) s x = 1. c. Since T i is just a standardized version of Y i , its mean and variance are also 0 and 1, respectively. d. Variance of ee . Here, X=log(food expenditure). Evaluated at s x 2 2 X , this yields . Therefore, the std of e . . e 821 2 2 46 2861746 = X 2861746 =1692. Note that this approximates the std of food expenditure. In order to compare this to the standard deviation of F from the table, we must adjust the units. Log(food expenditure) (LF) uses food expenditure data in \$1983, while food expenditure (F) uses data in 1,000’s of \$1983. So, we must divide the std we got by 1000 (=1.692) to put it into \$1983. Compare 1.692 to the std of F from the table, which is 1.85. The approximation is about 9% lower than the actual.

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

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

{[ snackBarMessage ]}

### Page1 / 4

s07pre1a - Prof G Jakubson Economics 321 Spring 2007...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online