HP 50g Graphing Calculator - Manual (Page 607)

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