1. This problem is to provide some intuition behind the CSRF (cumulative square root of the frequency) method briefly discussed at the end of Lec- ture 7, and why equal sample sizes for each stratum was recommended in Example 5.19. I will use the same set-up as Example 5.19 but change the numbers. The information we are provided is as follows. Income (thousands) 100-150 Frequency 25 150-200 25 200-250 25 250-300 9 300-350 9 350-400 400-450 450-500 6666 9 9 9 (a) How would you combine the 8 income intervals in L using the CSRF method? = 2 stratum (b) Assume that σ¿ is proportional to the number of intervals contained in the ith stratum. Thus for example if stratum 1 contains the first two intervals and stratum 2 contains the last six intervals, then σ1 = = 2\ = and σ2 6 for some unknown A. Show that for the stratification in 1(a), Neyman allocation recommends allocating equal sample sizes to the two strata. Remark: This exercise can be extended to any two integers u and v. That is if there are u + v intervals with a frequency of v² for each of the first u intervals, and a frequency of u² for each of the last v intervals, then applying CSRF and Neyman allocation for L 2 would lead to equal sample sizes to the two strata. =
1. This problem is to provide some intuition behind the CSRF (cumulative square root of the frequency) method briefly discussed at the end of Lec- ture 7, and why equal sample sizes for each stratum was recommended in Example 5.19. I will use the same set-up as Example 5.19 but change the numbers. The information we are provided is as follows. Income (thousands) 100-150 Frequency 25 150-200 25 200-250 25 250-300 9 300-350 9 350-400 400-450 450-500 6666 9 9 9 (a) How would you combine the 8 income intervals in L using the CSRF method? = 2 stratum (b) Assume that σ¿ is proportional to the number of intervals contained in the ith stratum. Thus for example if stratum 1 contains the first two intervals and stratum 2 contains the last six intervals, then σ1 = = 2\ = and σ2 6 for some unknown A. Show that for the stratification in 1(a), Neyman allocation recommends allocating equal sample sizes to the two strata. Remark: This exercise can be extended to any two integers u and v. That is if there are u + v intervals with a frequency of v² for each of the first u intervals, and a frequency of u² for each of the last v intervals, then applying CSRF and Neyman allocation for L 2 would lead to equal sample sizes to the two strata. =
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:1. This problem is to provide some intuition behind the CSRF (cumulative
square root of the frequency) method briefly discussed at the end of Lec-
ture 7, and why equal sample sizes for each stratum was recommended in
Example 5.19. I will use the same set-up as Example 5.19 but change the
numbers. The information we are provided is as follows.
Income (thousands)
100-150
Frequency
25
150-200
25
200-250
25
250-300
9
300-350
9
350-400
400-450
450-500
6666
9
9
9
(a) How would you combine the 8 income intervals in L
using the CSRF method?
= 2 stratum
(b) Assume that σ¿ is proportional to the number of intervals contained in
the ith stratum. Thus for example if stratum 1 contains the first two
intervals and stratum 2 contains the last six intervals, then σ1 = = 2\
=
and σ2
6 for some unknown A. Show that for the stratification in
1(a), Neyman allocation recommends allocating equal sample sizes
to the two strata.
Transcribed Image Text:Remark: This exercise can be extended to any two integers u and v. That
is if there are u + v intervals with a frequency of v² for each of the first
u intervals, and a frequency of u² for each of the last v intervals, then
applying CSRF and Neyman allocation for L 2 would lead to equal
sample sizes to the two strata.
=
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