Answer:
Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.
Step-by-step explanation:
Let p be the probability of heads in a single toss of the coin. Then our null hypothesis that the coin is fair will be formulated as 
H0 :p 0.5   against   Ha: p ≠ 0.5
The significance level is approximately 0.05
The test statistic to be used is number of heads x.
Critical Region: First we compute the probabilities associated with X the number of heads using the binomial distribution 
Heads (x)        Probability (X=x)                        Cumulative     Decumulative
0                        1/16384 (1)             0.000061     0.000061
1                         1/16384  (14)         0.00085             0.000911
2                       1/16384 (91)           0.00555             0.006461
3                       1/16384(364)         0.02222
4                       1/16384(1001)         0.0611
5                       1/16384(2002)       0.122188
6                        1/16384(3003)      0.1833
7                         1/16384(3432)      0.2095
8                        1/16384(3003)       0.1833
9                        1/16384(2002)       0.122188
10                       1/16384(1001)        0.0611
11                       1/16384(364)        0.02222
12                      1/16384(91)            0.00555                             0.006461
13                     1/16384(14)              0.00085                           0.000911
14                       1/16384(1)            0.000061                            0.000061
We use the cumulative and decumulative column as the critical region is composed of two portions of area ( probability) one in each tail of the distribution. If  alpha = 0.05 then alpha by 2 - 0.025 ( area in each tail).
We observe that P (X≤2) =   0.006461 > 0.025
and 
P ( X≥12 ) = 0.006461 > 0.025
Therefore true significance level is 
∝=  P (X≤0)+P ( X≥14 ) = 0.000061+0.000061= 0.000122
Hence critical region is (X≤0) and ( X≥14)
Computation x= 12 
Since x= 12 (0.006461) does not fall in the critical region so we accept our null hypothesis and conclude that the coin is fair.