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In Chapter 17 we use the numerical solver to solve the equation α =
UTPC(γ,x). In this program, γ represents the degrees of freedom (n-1), and α
represents the probability of exceeding a certain value of x (χ
2
χ
] = α.
α
For the present example, α = 0.05, γ = 24 and α = 0.025.
equation presented above results in χ
On the other hand, the value χ
values γ = 24 and α = 0.975.
12.4011502175.
The lower and upper limits of the interval will be (Use ALG mode for these
calculations):
2
/ χ
2
(n-1)⋅S
= (25-1)⋅12.5/39.3640770266 = 7.62116179676
α
n-1,
/2
2
2
/ χ
(n-1)⋅S
= (25-1)⋅12.5/12.4011502175 = 24.1913044144
α
n-1,1-
/2
Thus, the 95% confidence interval for this example is:
7.62116179676 < σ
Hypothesis testing
A hypothesis is a declaration made about a population (for instance, with
respect to its mean). Acceptance of the hypothesis is based on a statistical
test on a sample taken from the population.
decision-making are called hypothesis testing.
The process of hypothesis testing consists on taking a random sample from the
population and making a statistical hypothesis about the population. If the
observations do not support the model or theory postulated, the hypothesis is
rejected. However, if the observations are in agreement, then hypothesis is
not rejected, but it is not necessarily accepted.
is a level of significance α.
2
= χ
2
= 39.3640770266.
α
0.025
n-1,
/2
24,
2
2
= χ
is calculated by using the
α
0.975
n-1,
/2
24,
χ
2
The result is
2
< 24.1913044144.
The consequent action and
Associated with the decision
2
2
), i.e., Pr[χ
>
Solving the
= χ
2
=
α
0.975
n-1,1-
/2
24,
Page 18-34
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