The NFL needs to buy a new batch of official coins for the pre-game coin flip. T

Question

The NFL needs to buy a new batch of official coins for the pre-game coin flip. They get 3 sample coins from a manufacturer based in Sweden, and tell their intern to flip 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% significance, what is your conclusion?

Explanation / Answer

probabilty of 0 heads out of 3 =0.125

probabilty of 1 heads out of 3 =0.375

probabilty of 2 heads out of 3 =0.375

probabilty of 3 heads out of 3 =0.125

hence null hypothesis: p(0head)=0.125; p(1head)=0.375 ;p(2head)=0.375;p(3head)=0.125

alternate hypothesis: proportion are different then null hypothesis; mean coins are unfair

hence applying chi distribution goodness of fit:

for above test stat 10.1778 ; p value =0.0171

as p vlaue is less then 0.05, we reject null hypothesis and conclude that coins are unfiar.

observed Expected Chi square head Probability O E=total*p =(O-E)^2/E 0 0.125 7.00 3.75 2.82 1 0.375 7.00 11.25 1.61 2 0.375 8.00 11.25 0.94 3 0.125 8.00 3.75 4.82 30 30 10.1778

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