Inferences Concerning Two Variances - HP 50g User Manual

The test criteria are the same as in hypothesis testing of means, namely,
Reject H if P-value <
o
Do not reject H
Please notice that this procedure is valid only if the population from which the
sample was taken is a Normal population.
Example 1 -- Consider the case in which
20, and the sample was drawn from a normal population. To test the
hypothesis, H :
o
With = n - 1 = 25 - 1 = 24 degrees of freedom, we calculate the P-value as,
P-value = P(
Since, 0.2587... > 0.05, i.e., P-value > , we cannot reject the null hypothesis,
2
H : =25(=
o

Inferences concerning two variances

The null hypothesis to be tested is , H
)100%, or significance level , using two samples of sizes, n
2
variances s and s
1
as
2
where s and s
N
respectively. Selection of the numerator and denominator depends on the
alternative hypothesis being tested, as shown below. The corresponding F
distribution has degrees of freedom,
n , are the sample sizes corresponding to the variances s
D
respectively.
if P-value > .
o
2 2
= , against H
o
2
<
2
).
o
2
. The test statistic to be used is an F test statistic defined
2
2
represent the numerator and denominator of the F statistic,
D
2
= 25, =0.05, n = 25, and s
o
2 2
: < , we first calculate
1 o
) = 1-UTPC(24,
2 2
: =
o 2
2
s
F
N
o
2
s
D
= n -1, and
N N
) = 0.2587...
, at a level of confidence (1-
and n
1
= n -1, where n
D D
2
and s
N
2
=
, and
2
and
N
2
,
D
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