Up:
Stat 5132
Final
Problem 1
The test statistic is
Under the null hypothesis
Z
is standard normal.
From Table I in Lindgren, the onetailed
P
value is 0.0537.
Problem 2
Welch's procedure uses the test statistic
Under the null hypothesis
T
has an approximate Student
t
distribution with noninteger d. f. given by
From Table IIIa in Lindgren, the onetailed
P
value is 0.041 and the twotailed is (double that) 0.082. (The
exact
P
value using a computer is 0.081.)
Problem 3
The test statistic
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View Full Documenthas an asymptotic standard normal distribution under the null hypothesis
.For an
level
uppertail test, we reject when
Z
> 1.6449 (Table 1a in Lindgren).
Under the alternative hypothesis
is approximately standard normal. We don't know what
S
will be. In order to do a calculation we plug in the
estimate from preliminary data (
S
= 4).
The power condition is
where
P
A
here means probability under the alternative
(under which
Z
A
is standard normal). From
Table 1a in Lindgren we see that
P
A
(
Z
A
> 1.2816) = 0.9 so we find
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 Spring '02
 Staff
 Normal Distribution, Standard Deviation, Variance, Null hypothesis, Lindgren

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