Module H6 Practical 7
Estimation with Stratified Random Sampling
1. A survey of dairy farming is to be carried out in a region divided into four geographical
strata according to its major agricultural enterprise. One item of interest in the survey is
the total amount of milk production (litres) per day.
From a previous survey, the estimated standard deviations and the number of farms within
each stratum are known and appear below.
Stratum (i)
Ni
Si (litres)
Dairy
197
24.9
Cash grain
162
22.5
Livestock
427
19.3
Pasture
154
6.5
Total
Population
940
Proportional (ni)
Neyman’s (ni)
If costs of sampling are about the same in each stratum, but resources permit sampling
only about 300 farms in total, find the sample sizes in each stratum under
(a) proportional allocation;
(b) Neyman’s allocation.
Show your computations and enter your answers in the table above
SADC Course in Statistics
Module H2 Practical 7 – Page 1
Module H6 Practical 7
2. A district has 2072 farms which have been divided up into five strata on the basis of
area in acres. The table below (also available in the Excel worksheet cattle, in file
H6_data.xls) gives the number Ni of farms in a stratum, the size ni of the simple random
sample of farms taken n each stratum, the mean number of cattle per farm for each
stratum and the stratum variances of number of cattle per farm. This is of course a
summary of the raw data which consists of 500 observations (farms), and cattle numbers in
each farm.
Stratum (i)
Ni
ni
xi
si2
16
635
84
4.24
27.54
>16 to 30
570
125
11.63
55.84
>30 to 50
475
138
15.95
71.70
>51 to 75
303
112
23.59
192.32
89
41
29.61
334.93
2072
500
>75
Totals
(a) Estimate the mean number of cattle per farm and the total number of cattle in the
district.
(b) Calculate the standard error of the above two estimates and determine 95% confidence
intervals for both.
(c) Interpret your results and comment on the precision of your sample estimates. Also
comment on whether you would have had lower precision had you taken a simple random
sample instead of 500 farms. Explain your answer.
SADC Course in Statistics
Module H2 Practical 7 – Page 2
Module H6 Practical 7
3. Following an immunisation campaign, a survey was carried out in a rural area with 5
villages (strata) by selecting a simple random sample of 10 children aged 1 to 2 years from
each village and asking their parents about the child’s vaccination status. The data were as
follows:
Village (i)
Total number of
children aged 1-2 years
Number vaccinated
in selected sample
1
22
5
2
65
7
3
28
4
4
25
8
5
43
2
Total
183
(a) Estimate the proportion of children aged 1-2 in the area who have been vaccinated.
(b) Find also the standard error of your estimate and hence derive a 95% confidence
interval for the true proportion of children aged 1-2 who have been vaccinated.
(c) Comment on the results and the effectiveness of the immunisation campaign.
SADC Course in Statistics
Module H2 Practical 7 – Page 3