HP 48GII, Руководство пользователя, Страница: 608 / 864

Page 18-37
First, we calculate the appropriate statistic for the test (t
o
or z
o
) as follows:
•
If n < 30 and the standard deviation of the population,
σ
, is known,
use the z-statistic:
n
x
z
o
o
/ σ
µ −
=
•
If n > 30, and
σ
is known, use z
o
as above. If
σ
is not known,
replace s for
σ
in z
o
, i.e., use
n s
x
z o
o
/
µ −
=
•
If n < 30, and
σ
is unknown, use the t-statistic
n s
x
t
o
o
/
µ −
=
, with
ν
=
n - 1 degrees of freedom.
Then, calculate the P-value (a probability) associated with either z
ο
or t
ο
, and
compare it to
α
to decide whether or not to reject the null hypothesis. The P-
value for a two-sided test is defined as either
P-value = P(|z|>|z
o
|), or, P-value = P(|t|>|t
o
|).
The criteria to use for hypothesis testing is:
•
Reject H
o
if P-value <
α
•
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:
•
If using z, P-value = 2
⋅
UTPN(0,1,|z
o
|)
•
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