HP 49g+ - Manual (Page 606)

Page 18-39
• If using z, P-value = UTPN(0,1,z
o
)
• If using t, P-value = UTPT( ν,t
o
)
Example 2 -- Test the null hypothesis H
o
: µ = 22.0 ( = µ
o
), against the
alternative hypothesis, H
1
: µ >22.5 at a level of confidence of 95% i.e., α =
0.05, using a sample of size n = 25 with a mean x = 22.0 and a standard
deviation s = 3.5. Again, we assume that we don't know the value of the
population standard deviation, therefore, the value of the t statistic is the same
as in the two-sided test case shown above, i.e., t
o
= -0.7142, and P-value, for
ν = 25 - 1 = 24 degrees of freedom is
P-value = UTPT(24, |-0.7142|) = UTPT(24,0.7124) = 0.2409,
since 0.2409 > 0.05, i.e., P-value >
α, we cannot reject the null hypothesis
H
o
: µ = 22.0.
Inferences concerning two means
The null hypothesis to be tested is H
o
: µ
1
- µ
2
= δ, at a level of confidence (1-
α)100%, or significance level α, using two samples of sizes, n
1
and n
2
, mean
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
2
2
2
1
2
1
2 1
) (
n n
x x
z
o
σ σ
δ
+
− −
=
If n
1
< 30 or n
2
< 30 (at least one small sample), use the following test statistic:
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