1.  These data were on the midterm.  The Federal Highway Commission sampled households in the South and the Midwest to try to estimate the annual vehicle miles traveled (VMT).  We wish to determine if there are differences in "typical" VMTs in the South and Midwest.  Here are the data, in thousands of miles per year:
Midwest: 9.6, 10.8, 11.2, 12.9, 14.6, 15.1,16.2,16.6, 16.6, 17.3, 18.3, 18.6, 20.3, 20.9, 24.4
South: 9.3, 11.5, 12.2, 15.8, 16.0, 17.5, 18.0, 18.2, 19.2, 20.1, 20.2, 22.2, 22.8, 24.6
 

a) Make histograms for both the Midwest and the South.  (Note: this data is in ActivStats if you want to use the "Guide" to find it and upload it into DataDesk.)
Describe the shapes.  How do the histograms compare?
b) Make side-by-side boxplots and/or stem-and-leaf plots.  What do these plots suggest?
c) Assume that VMT in each region (South and M.West) follows a normal distribution.  Find 95% confidence intervals for the mean VMT for each region.
d)  Find a 95% confidence interval for the difference in the mean VMT between the two regions.  Assume the distribution of VMT for both groups is normal.  Based on this confidence interval, what do you conclude about the mean VMTs for the two regions?
e) Design and carry out a simulation that performs the median test.  What is your conclusion about VMTs?  Note that you did not need to assume normality to do this test!
 
 

2.  Return to the systolic blood pressure data.  These data are  systolic blood pressures (for 15 patients with moderate essential hypertension) taken immediately before and two hours after taking 25 mg of the drug captopril.  We can't determine whether the drug is effective without comparing to a control group, but lets see if there is any evidence in this data set that offers some hope that the drug is effective.
a) Create a new variable, call it "dif" that is After - Before.
b) Make a histogram of "dif".  What does it say about the drug's effectiveness?
c) Find a 95% confidence interval for the mean of dif.  What does it say about the drug's effectiveness?
d) Perform a t-test to test whether the drug is effective.  You should follow these steps:
i) State the null and alternative hypotheses.  These should be statements about the mean of the population.
ii) Compute the test statistic.
iii) Compute the p-value.
iv) Make a decision

3. For the same data.  Design and carry out the sign test to test whether the median change in blood pressure is negative or zero.  Show all steps.  (See pg. 494).