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Critical Thinking: Did the NFL Rule Change Have the Desired Effect? Among 460 overtime National Football League (NFL) games between 1974 and 2011, 252 of the teams that won the overtime coin toss went on to win the game. During those years, a team could win the coin toss and march down the field to win the game with a field goal, and the other team would never get possession of the ball. That just didn’t seem fair. Starting in 2012, the overtime rules were changed. In the first three years with the new overtime rules, 47 games were decided in overtime and the team that won the coin toss won 24 of those games. Analyzing the Results

What do you conclude about the effectiveness of the overtime rule change?

Short Answer

Expert verified

It can be concluded that the overtime change rule was not effective in reducing the number of overtime games that were won by the team that won the toss.

Step by step solution

01

Given information

In the years between 1974 and 2011, out of 460 overtime games, 252 games were won by the team that won the coin toss.

In the first 3 years beginning from 2012, there were 47 overtime games and 24 of those games were won by the team that won the coin toss.

02

Conclusion about the effectiveness of the overtime rule change

The number of overtime games that were won by the team that won the toss before the overtime rule change was not significantly greater than the number of overtime games that were won by the team that won the toss after the overtime rule change

This was proved by conducting the hypothesis test as well as the confidence interval in the previous exercise 2FDD.

Thus, it can be concluded that the overtime change rule was not effective in lowering the number of games that were won because of practising the unfair procedure that was prevalent before the rule was changed.

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Most popular questions from this chapter

Testing Claims About Proportions. In Exercises 7–22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.

Smoking Cessation Programs Among 198 smokers who underwent a “sustained care” program, 51 were no longer smoking after six months. Among 199 smokers who underwent a “standard care” program, 30 were no longer smoking after six months (based on data from “Sustained Care Intervention and Postdischarge Smoking Cessation Among Hospitalized Adults,” by Rigotti et al., Journal of the American Medical Association, Vol. 312, No. 7). We want to use a 0.01 significance level to test the claim that the rate of success for smoking cessation is greater with the sustained care program.

a. Test the claim using a hypothesis test.

b. Test the claim by constructing an appropriate confidence interval.

c. Does the difference between the two programs have practical significance?

Verifying requirements in the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group considered of 201,229 children given the sulk vaccine for polio, and 33 of those children developed polio. The other 200,745 children were given a placebo, and 115 of those children developed polio. If we want to use the methods of this section to test the claim that the rate of polio is less for children given the sulk vaccine, are the requirements for a hypothesis test satisfied? Explain.

Refer to Exercise 10.83 and find a 90 % confidence interval for the difference between the mean numbers of acute postoperative days in the hospital with the dynamic and static systems.

In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of\({n_1} - 1\)and\({n_2} - 1\).) Is Old Faithful Not Quite So Faithful? Listed below are time intervals (min) between eruptions of the Old Faithful geyser. The “recent” times are within the past few years, and the “past” times are from 1995. Does it appear that the mean time interval has changed? Is the conclusion affected by whether the significance level is 0.05 or 0.01?

Recent

78

91

89

79

57

100

62

87

70

88

82

83

56

81

74

102

61

Past

89

88

97

98

64

85

85

96

87

95

90

95

In Exercises 5–20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with “Table” answers based on Table A-3 with df equal to the smaller of n1−1 and n2−1.)

Color and Cognition Researchers from the University of British Columbia conducted a study to investigate the effects of color on cognitive tasks. Words were displayed on a computer screen with background colors of red and blue. Results from scores on a test of word recall are given below. Higher scores correspond to greater word recall.

a. Use a 0.05 significance level to test the claim that the samples are from populations with the same mean.

b. Construct a confidence interval appropriate for the hypothesis test in part (a). What is it about the confidence interval that causes us to reach the same conclusion from part (a)?

c. Does the background color appear to have an effect on word recall scores? If so, which color appears to be associated with higher word memory recall scores?

Red Background n = 35, x = 15.89, s = 5.90

Blue Background n = 36, x = 12.31, s = 5.48

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