\magnification=\magstep1
\centerline{MONT 103N -- Analyzing Environmental Data}
\centerline{Hypothesis Testing Practice Problems}
\centerline{April 18, 2012}
\bigskip
\noindent
{\it Directions:}  For each question, first identify
the relevant null and alternative hypotheses.  Then
carry out the appropriate hypothesis test, estimate the 
$p$-value if possible with the information you have, and answer
the other questions.  
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\item{1)}   The average $CO_2$ emissions for
a collection of 100 large power plants 
is $\overline{Y} = 2223.1$ lb/Mwh, with $SD = 211.3$ lb/Mwh.
\bigskip
\itemitem{a)}  If this were a random sample, would there
be evidence at the $\alpha = .05$ level
to say that the average coal-fired power plant
emits an amount different from $2200$ lb/Mwh?
\itemitem{b)}  This comes from a data set in our
textbook given in problem 15 on page 321.
Is this a random sample?  Does the calculation
in part a) really make sense in this setting?
\bigskip
\item{2)}  In a simple random sample of 2000 Germans in 2001, 
840 out of the 2000 thought that all electricity should be
generated by ``green'' energy sources such as wind and 
solar power.  Is there evidence at the $\alpha = .05$ level
to say that at least $40\%$ of all Germans thought the
same about sources of electric power?
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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 at the $\alpha = .05$ level
to say that the population arm length is different 
from $7$ cm?  (Note:  The short $t$-table on page 316 of the 
text has the information you need for this one, but it
will not be possible to estimate the $p$-value with 
only the information there.  Use the $t$-table demonstrated
in class to estimate this.)
\bigskip     
\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 at the $\alpha = .05$ level to say that
nonsmokers have a lower average pulse rate?   
\bye
