In the first election of the 20th century, Theodore Roosevelt (178 cm) defeated Alton B. Parker (175 cm). There have been 28 additional elections since then, for a total of 29. Of these, 26 elections had only two major party candidates with one taller than the other. In 20 of the 26 elections, the taller candidate won. 

a. Let π = P(taller wins). State the research hypothesis in words and in symbols. 

b. State the null and alternative hypotheses in words and symbols. 

c. Compute the appropriate p-value using an applet. 

d. If you take the p-value at face value, what do you conclude? 

e. Are there reasons not to take the p-value at face value? Is yes, list them.