10.1
Estimating with Confidence
10.4
A
UTO
E
MISSIONS
– Oxides of nitrogen (called NOX for short) emitted by cars and
trucks are important contributors to air pollution. The amount of NOX emitted by a
particular model varies from vehicle to vehicle. For one light truck model, NOX
emissions vary with mean
μ
that is unknown and standard deviation
σ
= 0.4 grams per
mile. You test an STS of 50 of these trucks. The sample mean NOX level χ estimates the
unknown
μ
. You will get different values of χ if you repeat your sampling.
(a)
Describe the shape, center, and spread of the sampling distribution of χ.
(b)
Sketch the normal curve for the sampling distribution of χ. Mark its mean and the
values one, two, and three standard deviations on either side of the mean.
(c)
According to the 98−75−99.7 rule, about 95% of all values of χ lie within a distance
m
of the mean of the sampling distribution. What is
m
? Shade the region on the axis
of your sketch that is within
m
of the mean.
(d)
Whenever χ falls in the region you shaded, the unknown population mean
μ
lies in
the confidence interval χ ±
m
. For what percent of all possible samples does this
happen?
(e)
Draw the confidence intervals below your sketch for two values of χ, one that falls
within the shaded region and one that falls outside it.
10.8
C
ORN
Y
IELD
– Crop researchers plant 15 plots with a new variety of corn. The yields
in bushels per acre are
138.0
139.1
113.0
132.5
140.7
109.7
118.9
134.8
109.6
127.3
115.6
130.4
130.2
111.7
105.5
Assume that
σ
= 10 bushels per acre.
(a)
Find the 90% confidence interval for the mean yield
μ
for this variety of corn. Use
your Inference Toolbox.
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 Spring '09
 Johnson
 Statistics, Algebra, Normal Distribution, Standard Deviation, Statistical hypothesis testing, mean IQ score

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