In a directory of 13 houses on the street the persons are listed as follows; M=a
ID: 2936057 • Letter: I
Question
In a directory of 13 houses on the street the persons are listed as follows; M=adult male; F = adult female; m = male child, f= female child. For a systematic sample, number down each column, then go to the top of the next column and continue numbering.
1-M,F,f,m,f
2-M,F,f,m,f
3-M,F,m,f
4-M,F
5-M,F,m,m,f
6-M,F,f,m
7-M,F,f,f,m
8-M,F,m,f
9-M,F,m
10-M,F,m,f
11-M,F,f,m
12-M,F,f
13-M,F
A. What would you expect for the proportion of males in a population?
B. Take a systematic sample of 5 from this list of 13 households, starting with #5. What is your estimate of the proportion of males?
C. Take a systematic sample of size 5 starting at a random location (assume it is location 3). What is your estimate of the proportion of males?
D. Discuss the difference in your two estimates for p-hat.
Explanation / Answer
a) Proportion of males in the population is 24/50= 0.48
b) Here we are taking systematic samples of size 5 from household number 5 is only house number 5th and house number 7th
Proportion of males for this systematic sampling= number of males in these two samples / total number of population = 5/ 50 = 0.1
c) Proportion of males from house number 3 with sample size 5
= 5/50= 1/10= 0.1
d) The difference between the two estimate that one is take from household number 3 (pre assumed) and one is from location starting with # 5.
Both Proportion estimates are equal.