Agriculture Reference
In-Depth Information
1.
Test for specified value of population mean
2.
Test of significance between two means:
(a)
We want to test
H
0
:
μ ¼
3,000 h against
H
1
:
Under the given condition σ
1
2
¼ σ
2
2
3,000 h.
The approximate test statistic under the given
condition is
μ 6¼
¼
2
σ
ð
unknown
Þ.
Under the given condition of σ
1
2
6¼ σ
2
2
(b)
and both being unknown.
τ ¼
x μ
0
2
;
890
3
;
000
¼
110
16
3.
Test for significance of specified popula-
tion standard deviation
¼
8
¼
55
:
00
:
s
n
n
16
64
=
p
p
4.
Test of significant difference between two
standard deviations
, that is, 55.00,
is greater than the table value of
τ
0
:
025
¼
1
:
96;
the test is significant and the null hypothesis is
rejected. So we conclude that the claim of the
manufacturer is not justified.
Thus, the calculated value of
jj
5.
Test for significance of specified popula-
tion proportion
6.
Test
for
equality of
two population
proportions
7.
χ
2
test
Example 9.17.
The manufacturer of certain
brand of water pump claims that the pump
manufactured by this company will fill a 1,000-l
water tank within 8 min with a variance of
9 min
2
. To test the claim, 36 pumps were exam-
ined and found that the average time taken to fill
tank is 10 min with s.d. 2.5 min. Conclude
whether the claim is justified or not.
1.
Test for Specified Value of Population Mean
Let a sample
x
n
be drawn at random
from a population with mean
x
1
,
x
2
,
...
,
μ
and variance
2
such that the size of the sample is
σ
30.
To test that whether the population mean
μ ¼ μ
0
, a specified value under (1) the popu-
lation variance
n
2
known and (2) the unknown
populati
o
n variance
σ
2
is the test statistics are
σ
Solution.
Given that (1) population mean (
μ
)
¼
τ ¼
xμ
0
σ=
2
is known and
(a)
p
, when
σ
2
)
9 min
2
.
8 min and variance (
σ
¼
τ ¼
xμ
0
s
n
=
2
is unknown,
(b)
p
, when
σ
(2) Sample size (
n
)
¼
36,
x ¼
10 min, and
P
i¼
1
2
s
n
¼
2.5 min.
Thus, under the given condition,
2
1
n
where
s
n
¼
ð
x
i
x
Þ
is the sample
the null
variance.
For acceptance or rejection of
hypothesis is
H
0
:
H
0
, we have to
compare the calculated value of
μ ¼
8 min against
with the
appropriate table value, keeping in view the
alternative hypotheses.
τ
8 min.
The test statistic is
H
1
:
μ >
τ ¼
x μ
0
Example
9.16.
A manufacturing company
claims that the average monthly salary of the
company is $3,000. To test this claim, a sample
of 64 employees were examined and found that
the average monthly salary was $2,890 with var-
iance 256 h. Test whether the claim is justified or
not using 5% level of significance.
σ=
n
p
which follows a standard normal distribution.
The calculated value of
10
8
2
τ ¼
=
3
p ¼
6
¼
4
:
3
=
3
Solution.
Given that (1) the sample is large
n
(
¼
30).
(2) Sample mean (
64
>
The calculated value of
jj¼
4
:
00 is greater
x
)
¼
2,890 and sample
than
96. So the test is significant and
the null hypothesis is rejected. Thus, we reject
τ
0
:
025
¼
1
:
variance
256.
(3) Population variance is unknown.
¼
