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\centerline{Mathematics 376 -- Probability and Statistics II}
\centerline{Discussion Day -- Specifying Tests of Hypotheses}
\centerline{March 17, 2006}
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{\it Background}
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Last time we introduced some basic terminology about
statistical tests of hypotheses -- the {\it null hypothesis}
$H_0$, the {\it alternative hypothesis} $H_a$, test statistic, the 
rejection region $RR$, and the Type I and Type II errors
and their probabilities, $\alpha$ and $\beta$ respectively.
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{\it Discussion Questions}
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Each group -- You have 20 minutes to analyze your assigned situation
to identify $H_0, H_a$ for a conjectural test that could be used
address the issue raised.  Also identify a test statistic
that you could compute from your samples, and which has
a {\it known distribution, at least approximately} (i.e. one of the ones fo
which we have tables in the text -- standard normal, $t$, $\chi^2$,
$F$, etc.)  Say what distribution your test statistic has.
When you are done, put up your results on the board.  
If you have time, think about some of the others too.
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Group 1.  It is claimed that the proportion of adult Americans who 
select jogging as one of their recreational activities
is $30\%$.  You are the public health department of
Sedentaria, a bedroom and retirement community outside
a major city and you want to determine if the proportion in your
town is actually lower.   You plan to conduct a 
survey of $500$ randomly selected adults to help answer 
the question.
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Group 2.  A previous survey showed that 20\% of the drivers in 
New Bumpshire, a state
without a mandatory seat-belt law, always wear seat-belts 
even though it is not required.  You are the New Bumpshire
State Police and 
you have now instituted public-service TV ads that are designed
to shock people into using seat-belts by showing gruesome auto
accidents where the drivers were seriously injured.  After the ads
have been on the air for 2 months, to determine
whether they are increasing the proportion of drivers
using their seat-belts, you randomly stop $500$
drivers and determine whether they are using their seat-belts.
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Group 3.  You are staff members
of {\it Update}, a national newsmagazine that has conducted a 
telephone poll of 800 adult Americans, 605 of them smokers.
The respondents were asked:
``Should the Federal tax on cigarettes be raised by \$1.25
to help pay for health care reform?''  You want to determine
whether the proportion of non-smokers who say yes is different
from the proportion of smokers who say yes.  
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Group 4.  The FVC (forced vital capacity) is the amount of 
air that a person can force out of his/her lungs in one 
exhalation.  The population mean FVC for adults is about 3.4
liters, and the FVC is normally distributed.  
You are the coaching staff of a college volleyball
team.  You want to assess the general physical fitness of your
team members by measuring their FVC's to determine
whether they are above average.  You test all $11$ team members.
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Group 5.  The mean birth weight of babies in the US is
3315 grams, and the birth weight is normally distributed, 
with standard deviation 300 grams. 
You are a biostatistical research team in Ghana trying to decide
whether mean birth weights in your country are different 
from those in the US.  You will have data from 1000 births
to use to make the comparison.  
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Group 6.  You are the statistical team at BigState U's 
School of Agriculture and Veterinary Medicine.  You 
want to study the variability of the number of pounds
of butterfat produced by your herd of Holstein cows in the 
305-day milking period after the birth of a calf.  
You have data on the butterfat production for 100 cows, and
you want to compare your herd's performance with that
of Northeastern Southwest U's herd, which had 
$\sigma^2 = 140$.  
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Group 7.  You are the quality-control team for DC Dullco, 
an auto parts manufacturer.  You regularly select 
self-sealing stembolts from the production line and
subject them to a torque test.  The goal is for the 
mean torque at failure of the stembolts to equal 125.
You select 100 stembolts one day, test them,
and want to determine if the goal is being met.
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Group 8.  You are a social psychology research team
at the Center for Advanced Social Studies.  
In the past, it was believed that $40\%$ of women
think all men are basically selfish.  You want to determine
whether the number is larger now.  You will design a survey
and interview 200 women to determine what they think.
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