A coin toss is used to decide which team gets the ball first

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 47 Super Bowl games, the National Football Conference has won the coin flip 31 times. Meanwhile, the American Football Conference has won only 16 times. Use the six-step hypothesis-testing procedure at the .01 significance level to test whether these data suggest a fair coin flip.

Make the decision rule. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Evaluate the test statistic. (Round your answer to 2 decimal places.)

What is the p-value? (Round your answer to 4 decimal places.)

Solution

(c) Given a=0.01, the critical values are Z(0.005) = -2.576 or 2.576 (from standard normal table)

Reject H₀ if z is not between -2.576 and 2.576

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(d)test statistic:

Z=(phat-p)/sqrt(p*(1-p)/n)

=(31/47-0.5)/sqrt(0.5*0.5/47)

=2.19

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(e) It is a two-tailed test.

So the p-value= 2*P(Z>2.19) =0.0285 (from standard normal table)