# Inferences Concerning Two Means - HP 50g User Manual

Graphing calculator.

Next, we use the P-value associated with either z or t , and compare it to
decide whether or not to reject the null hypothesis. The P-value for a two-sided
test is defined as either
The criteria to use for hypothesis testing is:
Reject H
if P-value <
o
Do not reject H
Notice that the criteria are exactly the same as in the two-sided test. The main
difference is the way that the P-value is calculated. The P-value for a one-sided
test can be calculated using the probability functions in the calculator as
follows:
If using z, P-value = UTPN(0,1,z
If using t, P-value = UTPT( ,t
Example 2 -- 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
deviation s = 3.5. Again, we assume that we don't know the value of the
population standard deviation, therefore, the value of the t statistic is the same
as in the two-sided test case shown above, i.e., t
= 25 - 1 = 24 degrees of freedom is
P-value = UTPT(24, |-0.7142|) = UTPT(24,0.7142) = 0.2409,
since 0.2409 > 0.05, i.e., P-value > , we cannot reject the null hypothesis H
= 22.0.

## Inferences concerning two means

The null hypothesis to be tested is H
)100%, or significance level , using two samples of sizes, n
P-value = P(z > |z
if P-value > .
o
:
>22.5 at a level of confidence of 95% i.e.,
1
|), or, P-value = P(t > |t
o
)
o
)
o
:
= 22.0 ( =
o
:
-
= , at a level of confidence (1-
o
1
2
|).
o
), against the
o
= -0.7142, and P-value, for
o
1
to
=
:
o
and n
, mean
2
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