HP 48gII - Manual (Page 611)

Page 18-40
Two-sided hypothesis
If the alternative hypothesis is a two-sided hypothesis, i.e., H
1
: µ
1
- µ
2
≠ δ, The
P-value for this test is calculated as
•
If using z, P-value = 2 ⋅UTPN(0,1, |z
o
|)
• If using t, P-value = 2 ⋅UTPT(ν,|t
o
|)
with the degrees of freedom for the t-distribution given by
ν = n
1
+ n
2
- 2. The
test criteria are
•
Reject H
o
if P-value < α
• Do not reject H
o
if P-value > α.
One-sided hypothesis
If the alternative hypothesis is a two-sided hypothesis, i.e., H
1
: µ
1
- µ
2
< δ, or,
H
1
: µ
1
- µ
2
< δ,, the P-value for this test is calculated as:
•
If using z, P-value = UTPN(0,1, |z
o
|)
• If using t, P-value = UTPT( ν,|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.
Paired sample tests
When we deal with two samples of size n with paired data points, instead of
testing the null hypothesis, H
o
: µ
1
- µ
2
= δ, using the mean values and standard
deviations of the two samples, we need to treat the problem as a single
sample of the differences of the paired values. In other words, generate a
new random variable X = X
1
-X
2
, and test H
o
: µ = δ, where µ represents the
mean of the population for X. Therefore, you will need to obtain x and s for
the sample of values of x. The test should then proceed as a one-sample test
using the methods described earlier.