STAT 350
Solutions to the Homework 9
61.
(a)
Let
μ
denote the true average soil heat flux covered with coal dust. The sample mean and standard
deviation of this data are
= 30.79 and s = 6.530. The relevant hypotheses are H
0
:
μ
=29.0 versus H
a
:
μ
>
29.0 and the calculated test statistic value is t =
=
= .775. For d.f. = n1 = 81 = 7, the
Pvalue
≈
.225 (from Table VI), so we would not reject H
0
at significance level
α
= .05. Therefore it can not
be concluded that coal dust increases the true average heat flux.
62.
(a)
No, it does not appear plausible that the distribution is normal. Notice that the mean value,
= 215,
is not nearly in the middle of the range of values, 5 to 1176. The midrange would be about 585.
Since the mean is so much lower than this, one would suspect the distribution is positively skewed.
However, it is not necessary to assume normality if the sample size is “large enough”, due to the
central limit theorem.
Since this problem has a sample size which is “large enough” (i.e., 47 > 30), we
can proceed with a test of hypothesis about the true mean consumption.
(b)
Let
denote the true mean consumption. Since we are interested in determining if there is
evidence to contradict the prior belief that
was at most 200 mg, the following hypotheses should
be tested.
H
0
:
= 200 versus H
a
:
> 200.
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 Spring '08
 Staff
 Statistics, Standard Deviation

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