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Next, we use the P-value 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:
Θ Reject H
o
if P-value < α
Θ Do not reject H
o
if P-value > α.
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:
Θ If using z, P-value = UTPN(0,1,z
o
)
Θ If using t, P-value = UTPT(ν,t
o
)
Example 2
-- Test the null hypothesis H
o
: μ = 22.0 ( = 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
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
o
= -0.7142, and P-value, for ν
= 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 > α, we cannot reject the null hypothesis H
o
:
μ = 22.0.
Inferences concerning two means
The null hypothesis to be tested is H
o
: μ
1
-μ
2
= δ, at a level of confidence (1-
α)100%, or significance level α, using two samples of sizes, n
1
and n
2
, mean