HP 50g User Manual page 605

The criteria to use for hypothesis testing is:
Reject H if P-value <
o
Do not reject H
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
If using t, P-value = 2 UTPT( ,|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
deviation s = 3.5. We assume that we don't know the value of the population
standard deviation, therefore, we calculate a t statistic as follows:
The corresponding P-value, for n = 25 - 1 = 24 degrees of freedom is
P-value = 2 UTPT(24,-0.7142) = 2 0.7590 = 1.518,
since 1.518 > 0.05, i.e., P-value > , we cannot reject the null hypothesis H
= 22.0.
One-sided hypothesis
The problem consists in testing the null hypothesis H
alternative hypothesis, H
)100%, or significance level , using a sample of size n with a mean x and a
standard deviation s. This test is referred to as a one-sided or one-tailed test.
The procedure for performing a one-side test starts as in the two-tailed test by
calculating the appropriate statistic for the test (t
if P-value > .
o
: 22.5, at a level of confidence of 95% i.e.,
1
x
t o
o
s / n
: > or H
1
|)
o
|)
o
: = 22.5 ( =
o
22 0 . 22 5 .
. 3 / 5 25
: < at a level of confidence (1-
1
or z
o
), against the
o
. 0 7142
: = , against the
o o
) as indicated above.
o
=
:
o
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