1. A research study aims to estimate the true mean income of employees in a certain small company.
There are 45 male and 55 female employees in this company. A stratified random sample of 10
employees, classified by sex, was selected without replacement. Data on their monthly income,
along with their age, have been collected
Respondent
Sex
Income (in Php 1000s)
Age (year)
1
M
60
35
2
F
45
28
3
M
75
40
4
F
55
32
5
M
80
45
6
F
65
38
7
M
50
29
8
F
70
42
9
M
55
33
10
F
60
36
a.
Estimate the true mean income of employees in the company using the traditional design-
based estimator. Give the estimated sampling variance of your estimate.
b. Suppose the 100 employees in the company aged 40 years, on average. Estimate the true
mean income of employees in the company using the ratio estimator considering the
sampling method. Give the estimated sampling variance of your estimate.
c. Measure the efficiency of the estimate in (b) relative to the estimate in (a).
d. Estimate the true proportion of 100 students whose monthly income is at least 70,000 pesos.
Compute its estimated standard error.