05 level (the table says
we need 10 or less). Note: data set 3 returns
p > .
05
with a ttest because the variability in sample “b” is
large. Data set 4 also returns
p > .
05 with a ttest
because the difference in sample means is small.
(c) For data set 3, MannWhitney test would be most
appropriate, because we are not sure the data are
normally distributed (presence of an ’outlier’ in sam
ple “b”) and the sample size in each sample is small
(4).
For data set 4, a ttest would be most appro
priate, because the normal distribution seems appro
priate in each sample and the ttest is more powerful
than MannWhitney test when both can be used.
3(a) Smaller with a onesided test in the correct direction.
The formula for
n
is
σ
2
(
z
α/
2
+
z
β
)
2
/
(
μ
0

μ
a
)
2
for a
2sided test, while we replace
z
α/
2
=
z
.
015
= 2
.
17
by
z
α
=
z
.
03
= 1
.
88 for a onesided test.
z
α
being
smaller,
n
is also smaller for a onesided test.
(b) Using
n
=
σ
2
(
z
α/
2
+
z
β
)
2
/
(
μ
0

μ
a
)
2
we get 25 =
104
*
(2
.
17 +
z
β
)
2
/
(0

5)
2
i.e.
z
β
=
√
6
.
01

2
.
17 =
0
.
281 and with Table A
β
=
.
3897 so the power is
61%. One can get the same result by determining the
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 Fall '08
 Staff
 Statistics, Binomial, Normal Distribution, Variance, 2sided test

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