1.   Following are the ages of a random sample of people who caught botulism (a potentially fatal form of food poisoning).  Find an 80% confidence interval for the mean age of all botulism sufferers.  Find a 90% confidence interval.  State your assumptions.
29, 39, 44, 37, 42, 17,38,43,51,30,32,59,33,31,32,32,36,50

2.  In 1992, a team of physicians challenged previous findings that set the mean healthy human body temperature at 98.6 degrees farenheit.  Suppose you were to collect a random sample of n people and measure their body temperature.  Assume body temperatures were normally distributed and had a SD of .8 degrees F.  At least how many people would you need in your sample if your 95%  confidence interval could only be .27 units wide?

3. A random sample of 2500 Republicans found that 52.2 % of them would vote for Elizabeth Dole if the elections were held today.  If the elections were held today, does this mean that Dole would necessarily win?  Find an approximate 99% confidence interval and see if it helps answer this question.
 

4.  Given the data in question 3, will Dole win the election if it were held today?  Phrase this question in terms of a null and alternative hypothesis.

5. A student once took a multiple choice test of 100 questions and got every question wrong!  The teacher was still impressed, however, because this meant that the student must have known something, because if he were just guessing he still would have got some right.  Assume that each question had 4 possible answers.  Write the null and alternative hypothesis.  Do you think the student was guessing?  Why?
 

6.  The 1992 physicians mentioned in problem 2 found that their sample had an average temperature of 98.2 degrees.  Assume that their sample consisted of 25 people (I don't know the details of this study, so I'm making them up) and the SD of this sample was 0.83.  Conventional medical wisdom was that the mean body temperature of healthy people was 98.6.  Do the data in this study contradict this?
    a) What is the population?
    b) What are the null and alternative hypotheses?
    c) What is the test statistic?
    d)  Suppose we wish to test at a significance level of 5%.  What are the critical value?
    e) What is the p-value?
    f) What is your conclusion?

7.  Perform a hypothesis test on the blood pressure data at the 5% level to test whether blood pressures did, in fact go down, or whether the observed change was consistent with what might be expected by chance alone.

8. A lawyer representing a group of minority employees wishes to make the argument that these employees were paid less, on average, than their non-minority counterparts.  If you had data to test this claim, would you use a one-sided or two-sided alternative hypothesis?