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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. =

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 4BGP
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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: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. =
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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