Question

2. At the start of overtime in a National Football League game, a coin is flipped to determine which team will kick off and which will receive. The question of interest is how much advantage (if any) is given to the team that wins the coin flip at the start of the sudden death overtime period. In the overtime games played between 1974 and 2009, the winner of the coin flip won the game in 240 of the 428 games in which a winner was determined in overtime. Assume that the overtime games played during this time period can be viewed as a sample of all possible NFL overtime games. Do the data provide sufficient evidence to conclude that the team winning the coin flip has an advantage in overtime games? Show all details of the test using the methods of Section 6.1-HT. Parameter: Hypotheses: Sample statistic: Test statistic: P-value: Conclusion (reject or do not reject): Conclusion in context:

Answer 1

240 The following information is provided: The sample size is N = 428, the number of favorable cases is X = 240, and the sample proportion is ő = À 0.5607 , and the significance level is a = 0.05 428 (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: p < 0.50 Ha: p > 0.50 This corresponds to a right-tailed test, for which a z-test for one population proportion needs to be used. (2) Rejection Region - -0.05, and the Based on the information provided, the significance level is a critical value for a right-tailed test is ze = 1.64. The rejection region for this right-tailed test is R= {z: z > 1.64} (3) Test Statistics The z-statistic is computed as follows: z = P - PO V Po(1 - Po)/n 0.5607 – 0.50 70.50(1 – 0.50)/428 2.514 (4) Decision about the null hypothesis 2.514 > 2c = 1.64, it is then concluded that the null Since it is observed that z = hypothesis is rejected. Using the P-value approach: The p-value is p = 0.006, and since p= = 0.006 < 0.05, it is concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population proportion p is greater than po, at the a = 0.05 significance level.

parameter is population proportion

sample statistic is 0.5607

in this hypothesis testing procedure we want to test weather more than 50% Times winner was determined. and finally we get that this claim is true.

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