HW 5 SOLUTIONS
Inference for Two Population Means
1. The Type II Error rate,
β
= P{failing to reject H
0
H
0
is false}, for a hypothesis test was calculated to be
β
=
0.07. What is the power = P{rejecting H
0
 H
0
is false} for this test?
Correct:
Power = 1 
β
= 1  0.07 = 0.93
2. Don is studying species of fish inhabiting a certain river. He fails to reject the null hypothesis that there are
an equal amount of species of fish found in the pools and in the riffles of this river.
Which of the following
statements is true?
Don may have made a Type I error.
Don definitely made a Type I error.
Don may have made a Type II error.
Don definitely made a Type II error.
Don definitely did not make either a Type I or a Type II error.
3. 7.38. Researchers studied the effect of a houseplant fertilizer on radish sprout growth. They randomly
selected some radish seeds to serve as controls, while others were planted in aluminum planters to which
fertilizer sticks were added. Other conditions were held constant between the two groups. The following table
shows data on the heights of plants (in cm) two weeks after germination.
Control
Fertilized
3.4 1.6
2.8
1.9
4.4 2.9
1.9
2.7
3.5 2.3
3.6
2.3
2.9 2.8
1.2
1.8
2.7 2.5
2.4
2.7
2.6 2.3
2.2
2.6
3.7 1.6
3.6
1.3
2.7 1.6
1.2
3.0
2.3 3.0
0.9
1.4
2.0 2.3
1.5
1.2
1.8 3.2
2.4
2.6
2.3 2.0
1.7
1.8
2.4 2.6
1.4
1.7
2.5 2.4
1.8
1.5
n
28
28
Y
ഥ
2.58
2.04
s
0.65
0.72
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View Full Documenta. Construct a 90% confidence interval for the difference in mean growth for the control and fertilizer groups.
Correct:
Note, this is the independent samples setting.
TI84
STAT>TESTS and 2SampTInt>Stats>Enter>scroll down to enter
x
1
: 2.58 Sx1: 0.65 n1: 28
x
2
: 2.04
Sx2:0.72 n2: 28 >CLevel 0.90> Pooled “NO”>Calculate>yields (0.233, 0.847)
b. Interpret the interval you just computed in part (a).
Correct:
We are 90% confident that the true mean height of radish plants two weeks after germination is bigger for
radishes with no fertilizer than for radishes grown with fertilizer by at least 0.235 cm and at most 0.851 cm.
c. Use the QQplot to assess the normality assumption for this
t
based interval.
Correct:
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 Fall '09
 Hendrix
 Statistics, Normal Distribution, Type I and type II errors, Student's tdistribution, mean cholesterol level

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