Agriculture Reference
In-Depth Information
Table 6.2
Sample size corresponding to different population sizes
Population
size (
Sample
size (
Population
size (
Sample
size (
Population
size (
Sample
size (
Population
size (
Sample
size (
N
)
n
)
N
)
n
)
N
)
n
)
N
)
n
)
10
10
150
108
460
210
2,200
327
15
14
160
113
480
214
2,400
331
20
19
170
118
500
217
2,600
335
25
24
180
123
550
226
2,800
338
30
28
190
127
600
234
3,000
341
35
32
200
132
650
242
3,500
346
40
36
210
136
700
248
4,000
351
45
40
220
140
750
254
4,500
354
50
44
230
144
800
260
5,000
357
55
48
240
148
850
265
6,000
361
60
52
250
152
900
269
7,000
364
65
56
260
155
950
274
8,000
367
70
59
270
159
1,000
278
9,000
368
75
63
280
162
1,100
285
10,000
370
80
66
290
165
1,200
291
15,000
375
85
70
300
169
1,300
297
20,000
377
90
73
320
175
1,400
302
30,000
379
95
76
340
181
1,500
306
40,000
380
100
80
360
186
1,600
310
50,000
381
110
86
380
191
1,700
313
75,000
382
120
92
400
196
1,800
317
100,000
384
130
97
420
201
1,900
320
140
103
440
205
2,000
322
Estimation of sample size in research using
Krejcie and Morgan's table is a commonly
employed method (Krejcie and Morgan 1970).
accuracy to base decisions on the findings with
confidence.
A
is a real valued function of the sample
values. For example, the sample mean
statistic
¼ y ¼
2
2
2
P
n
i¼
1
y
i
;
n
i¼
1
y
i
y
S ¼ χ
NP
ð
1
P
Þ=d
ð
N
1
Þ χ
P
ð
1
P
Þ
2
1
n
¼ s
0
2
1
n
sample variance
y
¼
ð
Þ
;
S ¼
the required sample size
¼ c
y
¼
s
0
y
sample coefficient of variation
y
:
2
χ
¼
the table value of chi-square for one degree
of freedom at the desired confidence level
is a statistic used to estimate the
population parameter and is a random variable as
its value differs from sample to sample, and the
samples are selected with specified probability
laws. The particular value, which the estimator
takes for a given sample, is known as an
An
estimator
N ¼
the population size
P ¼
the population proportion (assumed to be
.50 since this would provide the maximum
sample size)
estimate
.
d ¼
the degree of accuracy expressed as a pro-
portion (.05)
An estimator
t
is said to be an
unbiased esti-
mator
of parameter
θ
if
EðtÞ¼θ
, where
EðtÞ¼
P
M
0
i¼
1
i
th
sample is
p
i
,
and
t
i
(
i ¼
1, 2, 3
...
..
M
0
) is the
estimate, that is, the value of estimator “
t
i
p
i
Table
6.2
is given in DK Lal Das' Design of
Social Research for the purpose. Based on
Krejcie and Morgan's (1970) table for determin-
ing sample size, for a given population of 500, a
sample size of 217 would be needed to represent
a cross section of the population. However, it is
important for a researcher to consider whether
the sample size is adequate to provide enough
and the probability of getting the
t
” based
on this sample for the parameter
M
0
being the
total number of possible samples for the specified
probability scheme. On the other hand,
θ
,
if
EðtÞ 6¼ θ
, the estimator is said to be a
biased
