1. The lives of many people are affected by a fear that prevents them from flying. The Marist Institute for Public Opinion conducted a poll of 1014 adults , 48% of whom were men. The results reported in USA Today showed that 12% of the men and 33% of the women fear flying.

Analyzing the Results

1. How many men were surveyed? How many women were surveyed? How many of the surveyed men fear flying? How many of the surveyed women fear flying?
2. Is there sufficient evidence to conclude that there is a significant difference between the percentage of men and the percentage of women who fear flying?
3. Construct a 95% confidence interval estimate of the difference between the percentage of men and the percentage of women who fear flying. Do the confidence interval limits contain 0, and what is the significance of whether they do or do not?
4. Construct a 95% confidence interval for the percentage of men who fear flying.
5. Based on the result from the confidence interval obtained in (d) complete the following statement, which is typical of the statement that would be reported in the newspaper or magazine : "Based on the Marist Institute for Public Opinion poll, the percentage of men who fear flying is 12% with a margin of error of _____."
6. In a separate Gallup poll, 1001 randomly selected adults were asked this question: "If you had to fly on an airplane tomorrow, how would you describe your feelings about flying? Would you be – very afraid, somewhat afraid, not very afraid, or not afraid at all? Here are the responses: Very afraid (18%), somewhat afraid (26%) not very afraid (17%) not afraid at all (38%) and no opinion (1%). Are these Gallup poll results consistent with those conducted by the survey conducted by the Marist Institute? Explain. Can discrepancies be explained by the fact that the Gallup survey was conducted after the September 11 ^th terrorist attacks whereas the other survey was conducted before that date?
7. Construct a graph which would make the results understandable to the typical newspaper readers.

2. A good source for examples of paired data and the study of correlation is the field of medicine.  Medical researchers often seek to find relationships between two observed and measurable characteristics of a set of patients.  The site maintained by The Journal of Statistics Education contains a data archive that stores an interesting variety of data sets including some medical data.   In particular, there is a data set consisting of the heart rates (y) and body temperatures (x) for a group of people. I have put this data into a spreadsheet for you.

1. Compute the correlation coefficient between heart rate and body temperature using men only, and men and women (these are two separate calculations). Are the two quantities highly correlated?
2. Determine the line of best fit for the heart rate-body temperature data using temperature as the independent variable (for men AND women). Next determine the linear best fit using only the data corresponding to male subjects only. Use both linear formulas to predict the heart rate of a male with a body temperature of 98º F. Which prediction do you think is better? Why?

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