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hw5_soln-1

# hw5_soln-1 - Problem 4.12(a N = N i = 1000 = 10(1000 =...

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Problem 4.12 (a) 000 , 10 ) 1000 ( 10 1000 10 1 1 = = = = = = i k i i N N (b) Since we now require a confidence level of 90%, our z value is now . 645 . 1 = z Without any previous information about , i π we set 5 . 0 = i each stratum. Thus, 25 . ) 5 . 1 ( 5 . ) 1 ( 2 = - = - = i i i σ and 5 . 25 . = = i . Under the assumption of equal unit costs and variances, our minimum sample size is: = = + = k i i i B k i i i N N N n 1 2 2 645 . 1 2 2 1 ) ( 12 . 699 ) 25 )(. 1000 ( ) ( ) 000 , 10 ( ) 5 )(. 1000 ( 10 1 2 645 . 1 03 . 2 2 10 1 = + = = = i i , so round up to 700. Now, each stratum sample size is ) / ( N N n n i i = , but 10 . 000 , 10 / 1000 / = = N N i for each stratum. So 70 ) 10 )(. 700 ( = = i n for each stratum. (c) 70 / 5 1 = p , 70 / 4 2 = p , …, 70 / 8 10 = p 07857 . 70 55 10 . 70 8 70 4 70 5 10 . 10 . ) 10 (. 10 1 10 1 10 1 str = + + + = = = = = = = i i i i i i i p p N N p p (d) = - - - = k i i i i i i i i p n p p N n N N N s 1 2 2 2 1 ) 1 ( 1 = - - - = 10 1 and same the has stratum each since 2 2 ) 1 ( 1 1 1 i i i n N i i i i i p p n N n N N N i i k k k k k k k k k

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hw5_soln-1 - Problem 4.12(a N = N i = 1000 = 10(1000 =...

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