Errors In Hypothesis Testing - HP 50g User Manual

Notes:
1. For the example under consideration, the alternate hypothesis H
produces what is called a two-tailed test. If the alternate hypothesis is H
> 0 or H : -
1 1 2
2. The probability of rejecting the null hypothesis is equal to the level of
significance, i.e., Pr[T R|H
conditional probability of event A given that event B occurs.

Errors in hypothesis testing

In hypothesis testing we use the terms errors of Type I and Type II to define the
cases in which a true hypothesis is rejected or a false hypothesis is accepted
(not rejected), respectively. Let T = value of test statistic, R = rejection region, A
= acceptance region, thus, R A =
space for T, and
Type I or of Type II are as follows:
Rejecting a true hypothesis,
Not rejecting a false hypothesis, Pr[Type II error] = Pr[T A|H
Now, let's consider the cases in which we make the correct decision:
Not rejecting a true hypothesis, Pr[Not(Type I error)] = Pr[T A|H
Rejecting a false hypothesis,
The complement of
the alternative H
minimum sample size to restrict errors.
Selecting values of
A typical value of the level of significance (or probability of Type I error) is
0.05, (i.e., incorrect rejection once in 20 times on the average). If the
consequences of a Type I error are more serious, choose smaller values of ,
say 0.01 or even 0.001.
< 0, then we have a one-tailed test.
]= . The notation Pr[A|B] represents the
0
= the empty set. The probabilities of making an error of
Pr[Not(Type II error)] = Pr [T R|H
is called the power of the test of the null hypothesis H
. The power of a test is used, for example, to determine a
1
and
, and R A = , where
Pr[Type I error] = Pr[T R|H
: - 0
1 1 2
: -
1 1
= the parameter
] =
0
] =
1
] = 1 -
0
] = 1 -
1
vs.
0
=
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