Two coins are tossed 100 times and the following results wer

Two coins are tossed 100 times and the following results were obtained:

Number of            Times

         Heads           

      Occurred

Test at = 0.05 if the coins are fair

Solution

Using a binomial distribution, the probabilities of 0, 1, and 2 heads out of 2 fair coins is

P(0) = 0.25
P(1) = 0.50
P(2) = 0.25

Doing an observed/expected value table,
O E (O - E)^2/E
10 25 9
40 50 2
50 25 25

  
Using chi^2 = Sum[(O - E)^2/E],
  
chi^2 = 36
  
As df = a - 1,   
  
a = 3
df = a - 1 = 2
  
Then, the critical chi^2 value is
  
significance level = 0.05
chi^2(crit) = 5.991464547
  
Also, the p value is
  
p = 1.523E-08
  
Thus, comparing chi^2 and chi^2(crit) [or, p and significance level], we REJECT THE NULL HYPOTHESIS.

Thus, there is a significant evidence that the coin is not fair. [CONCLUSION]