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\centerline{MONT 105Q -- Mathematical Journeys}
\centerline{Hypothesis Testing Practice Problems}
\centerline{April 1, 2016}
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\noindent
{\it Directions:}  
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For each question, first identify and state
relevant null and alternative hypotheses.  Then
carry out the indicated hypothesis test, state your conclusions
briefly and cogently, and answer any other questions.  
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\item{1)}   The average $CO_2$ emissions for
a collection (sample) of 100 large power plants 
is $\overline{Y} = 2223.1$ lb/Mwh, with sample $SD = 211.3$ lb/Mwh.
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\itemitem{a)}  If this were a random sample, and 
we carried out a hypothesis test designed to make the 
probability of a Type I error equal $\alpha = .05$, would there be
sufficient evidence to say that the average coal-fired power plant
emits an amount greater than $2200$ lb/Mwh?
\itemitem{b)}  But now, suppose you knew that this data was collected
from just the 100 largest power plants in the country.
Is this a random sample?  Does the calculation
in part a) really make sense in this setting?
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\item{2)}  In a sample of $n = 50$ field mice caught in the wild,
the average body length (excluding the tails) was $\overline{Y} = 6.8$ cm with a 
sample SD $= .4$ cm.   With a hypothesis test designed to make the 
probability of a Type I error equal $\alpha = .05$, would there be
sufficient evidence to say that population body length is different 
from $7$ cm?  
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\item{3)} 
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 
$SD_2 = 4.9$.  With a hypothesis test designed to make the 
probability of a Type I error equal $\alpha = .01$, would there be
sufficient evidence to say that nonsmokers have a lower average pulse 
rate?   
\bye
