# HP F2226A - 48GII Graphic Calculator User Manual Page 608

Graphing calculator.

First, we calculate the appropriate statistic for the test (t
If n < 30 and the standard deviation of the population, σ, is known,
use the z-statistic:
If n > 30, and σ is known, use z
replace s for σ in z
If n < 30, and σ is unknown, use the t-statistic
n - 1 degrees of freedom.
Then, calculate the P-value (a probability) associated with either z
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
The criteria to use for hypothesis testing is:
if P-value < α
Reject H
o
Do not reject H
o
The P-value for a two-sided test can be calculated using the probability
functions in the calculator as follows:
If using z,
If using t,
Example 1 --
Test the null hypothesis H
alternative hypothesis, H
0.05, using a sample of size n = 25 with a mean x = 22.0 and a standard
x
z
=
o
σ
/
as above. If σ is not known,
o
x
z
=
, i.e., use
o
o
s
/
|), or, P-value = P(|t|>|t
o
if P-value > α.
P-value = 2⋅UTPN(0,1,|z
P-value = 2⋅UTPT(ν,|t
|)
o
: µ = 22.5 ( = µ
o
: µ ≠22.5, at a level of confidence of 95% i.e., α =
1
or z
) as follows:
o
o
µ
o
n
µ
o
n
x
µ
t
=
o
, with ν =
o
s
/
n
or t
ο
ο
|).
o
|)
o
), against the
o
Page 18-37
, and