User Guide

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
ns
x
z
o
o
/
µ−
=
• If n < 30, and σ is unknown, use the t-statistic
ns
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