A coin toss is used to decide which team gets the ball first in most sports. It involves little effort and is believed to give each side the same chance. In 45 Super Bowl games, the National Football Conference has won the coin flip 31 times. Meanwhile, the American Football Conference has won only 14 times. Use the five-step hypothesis-testing procedure at the 0.01 significance level to test whether this data suggest a fair coin flip.
a. Why can you employ z as the test statistic?
b. State the null and alternative hypotheses.
c. Make a diagram of the decision rule.
d. Evaluate the test statistic and make the decision.
e. Determine the p-value. What does this imply?