HP 50G, Руководство пользователя

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Page 18-40
values
⎯
x
1
and
⎯
x
2
, and standard deviations s
1
and s
2
. If the populations
standard deviations corresponding to the samples,
σ
1
and
σ
2
, are known, or if
n
1
> 30 and n
2
> 30 (large samples), the test statistic to be used is
If n
1
< 30 or n
2
< 30 (at least one small sample), use the following test statistic:
Two-sided hypothesis
If the alternative hypothesis is a two-sided hypothesis, i.e., H
1
:
μ
1
-
μ
2
≠ δ
, The P-
value for this test is calculated as
Θ
If using z, P-value = 2
⋅
UTPN(0,1, |z
o
|)
Θ
If using t, P-value = 2
⋅
UTPT(
ν
,|t
o
|)
with the degrees of freedom for the t-distribution given by
ν
= n
1
+ n
2
- 2. The
test criteria are
Θ
Reject H
o
if P-value <
α
Θ
Do not reject H
o
if P-value >
α
.
One-sided hypothesis
If the alternative hypothesis is a two-sided hypothesis, i.e., H
1
:
μ
1
-
μ
2
<
δ
, or,
H
1
:
μ
1
-
μ
2
<
δ
,, the P-value for this test is calculated as:
Θ
If using z, P-value = UTPN(0,1, |z
o
|)
Θ
If using t, P-value = UTPT(
ν
,|t
o
|)
2
2
2
1
2
1
2 1
) (
n n
x x
z
o
σ σ
δ
+
− −
=
2 1
2 1 2 1
2
2 2
2
1 1
2 1
) 2 (
) 1 ( ) 1 (
) (
n n
n n n n
s n s n
x x
t
+
− +
− + −
− −
=
δ