Assignment 6 Solutions
11.32. State:
How large an SRS is needed to reduce the standard deviation of
x
to 0.5 inch?
Formulate:
Use the formula for the standard deviation of the mean, and solve for the sample size.
Solve:
We need to choose
n
so that
2.8
/
n
=
0.5.
That means
n
=
5.6,
so
n
= 31.36.
Because
n
must be a whole number, take
n
= 32.
Conclude:
A sample of size 32 will give a standard deviation (slightly below) 0.5 inch.
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View Full Document14.10.
n
=
2.576
15
5
2
=
.
59.72
—take
n
= 60.
15.6.
H
0
:
μ =
20 min;
H
a
:
μ ≠
20 min.
15.19. State:
Do student SATM scores improve on their second attempt?
Formulate:
Let
μ
be the mean change in SATM score.
We test
H
0
:
μ =
0 versus
H
a
:
μ >
0; the
alternative is onesided because we expect scores to increase.
Solve:
We were told the 46 students were “randomly” chosen, and that we “know” that changes in
score follow a Normal distribution with standard deviation 50 points.
We find that
x
= 13.1087
points, so the test statistic is
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 Spring '10
 Kushner
 Statistics, Normal Distribution, Standard Deviation, 1%, mean IQ, 0.5 inch

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