# Paired Sample Tests, - HP 49g+ User Manual

Graphing calculator.

Two-sided hypothesis
If the alternative hypothesis is a two-sided hypothesis, i.e., H
P-value for this test is calculated as
If using z,
If using t,
with the degrees of freedom for the t-distribution given by ν = n
test criteria are
if P-value < α
Reject H
o
Do not reject H
o
One-sided hypothesis
If the alternative hypothesis is a two-sided hypothesis, i.e., H
: µ
< δ,, the P-value for this test is calculated as:
H
1
1
2
If using z,
If using t,
The criteria to use for hypothesis testing is:
if P-value < α
Reject H
o
Do not reject H
o
Paired sample tests
When we deal with two samples of size n with paired data points, instead of
testing the null hypothesis, H
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
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.
P-value = 2⋅UTPN(0,1, |z
P-value = 2⋅UTPT(ν,|t
|)
o
if P-value > α.
P-value = UTPN(0,1, |z
P-value = UTPT(ν,|t
|)
o
if P-value > α.
: µ
= δ, using the mean values and standard
o
1
2
: µ = δ, where µ represents the
-X
, and test H
1
2
o
: µ
≠ δ, The
1
1
2
|)
o
+ n
- 2. The
1
2
: µ
< δ, or,
1
1
2
|)
o
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