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\centerline{MONT 105N -- Analyzing Environmental Data}
\centerline{Practice Problems on Hypothesis Testing}
\centerline{April 8, 2019}
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{\it Directions}
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We'll make two ``passes'' on these problems.  
\item{$\bullet$}  In the first, we just want to identify what kind of test 
we will need (is it a test for a mean, or a proportion? large or small sample case?),
and identify appropriate
null and alternative hypotheses from the question that is asked.
\item{$\bullet$}  Then, in the second pass, we'll learn how to compute a test statistic, 
set up a rejection region, and 
decide whether we have enough evidence to reject the null hypothesis
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\noindent
{\it Questions}
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\item{1.}  $CO_2$ emissions per Megawatt-hour (Mwh) of electric
power produced were measured for $n = 100$ coal-fired power plants.
Assume this was a random sample of all such power plants in the 
U.S.  (there is a population of several thousand such power plants). 
The sample average $CO_2$ emissions per Megawatt-hour
is $\overline{Y} = 2223.1$ lb/Mwh, with sample $SD = 211.3$ lb/Mwh.  Is there
evidence to say that the population average coal-fired power plant
has $CO_2$ emissions per Mwh greater than $2100$ lb/Mwh?  
Test with $\alpha = .01$.
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\item{2.} In a telephone survey of 900 randomly selected adults 
in December 2018, 558 said
that they did not believe President Trump was being completely honest
about contacts between his Presidential campaign in 2016 and Russians.  
Is there evidence to say that fewer than 65\% of the adult residents
of the U.S. thought the same thing at that point in time?  Test with 
$\alpha = .05$.
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\item{3.}  In a study of $n = 17$ sea star arm lengths,
the average was $\overline{Y} = 6.8$ cm with an 
SD $= .5$ cm.  Is there evidence 
to say that the population arm length is different 
from $7$ cm?  Test with $\alpha = .05$. 
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\item{4.}
A medical study compared the resting pulse
rates of random, independent samples of 100 smokers and 100 nonsmokers.  The 
smokers had an average pulse rate of $\overline{Y} = 86$
beats per minute with $SD_1 = 5.4$, while the nonsmokers had an
average pulse rate of $\overline{X} = 80$ and $SD_2 = 4.9$.
Is there evidence to say that
nonsmokers have a lower average pulse rate?  Test with $\alpha = .05$
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\item{5.}  The data used in question 1 above actually comes
from the 100 largest coal-fired electric power plants in the U.S. (this is
true) at one point in the early 2000's.   Is this a random sample?  
Does the question and the calculation you did in question 4 
really make sense in this setting?  Discuss.
\bye
