HP 50G, User Manual

Page: 605 / 887

Page 18-38
The criteria to use for hypothesis testing is:
Θ
Reject H
o
if P-value <
α
Θ
Do not reject H
o
if P-value >
α
.
The P-value for a two-sided test can be calculated using the probability functions
in the calculator as follows:
Θ
If using z, P-value = 2
⋅
UTPN(0,1,|z
o
|)
Θ
If using t, P-value = 2
⋅
UTPT(
ν
,|t
o
|)
Example 1 -- Test the null hypothesis H
o
:
μ
= 22.5 ( =
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. We assume that we don't know the value of the population
standard deviation, therefore, we calculate a t statistic as follows:
The corresponding P-value, for n = 25 - 1 = 24 degrees of freedom is
P-value = 2
⋅
UTPT(24,-0.7142) = 2
⋅
0.7590 = 1.518,
since 1.518 > 0.05, i.e., P-value >
α
, we cannot reject the null hypothesis H
o
:
μ
= 22.0.
One-sided hypothesis
The problem consists in testing the null hypothesis H
o
:
μ
=
μ
o
, against the
alternative hypothesis, H
1
:
μ
>
μ
ο
or H
1
:
μ
<
μ
ο
at a level of confidence (1-
α
)100%, or significance level
α
, using a sample of size n with a mean
⎯
x and a
standard deviation s. This test is referred to as a one-sided or one-tailed test.
The procedure for performing a one-side test starts as in the two-tailed test by
calculating the appropriate statistic for the test (t
o
or z
o
) as indicated above.
7142 . 0
25 / 5 . 3
5 . 22 0 . 22
/
− =
−
=
−
=
n s
x
t o
o
μ