The NFL needs to buy a new batch of ocial coins for the pre-game coin ip. They g

Question

The NFL needs to buy a new batch of ocial coins for the pre-game coin ip. They get 3 sample coins from a manufacturer based in Sweden, and tell their intern to ip all 3 coins simultaneously multiple times and count the number of heads each time. The intern gets: 0 heads 7 times; 1 head 7 times; 2 heads 8 times; and 3 heads 8 times. Should the NFL buy coins from that manufacturer, i.e., are the coins fair or not? Perform the best test you can, making sure you clearly state your hypotheses and that you answer with a P-value. At 95% signicance, what is your conclusion

Explanation / Answer

Hypotheses:

Ho: The distribution is as per the expectation

Ha: The distribution is not as per the expectation; that is, it is different

Decision Rule:

= 0.05

Count = 4

Degrees of freedom =   4 - 1 = 3

Critical Value of 2 = 7.814727764

Reject Ho if 2 > 7.814727764

2 = 10.17777778   

p- value = 0.017113863   

Decision (in terms of the hypotheses):    

Since 10.17777778 > 7.814727764 we reject Ho

Conclusion (in terms of the problem):    

It appears that the distribution is not as per the expectation; that is, it is different. The coins are not fair and so should not be bought.

Test Statistic: Recorded Expected (Recorded - Expected)^2 / Expected 7 3.75 2.816666667 7 11.25 1.605555556 8 11.25 0.938888889 8 3.75 4.816666667 2 = 10.17777778

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