Recall the statistical experiment in which you flip a coin n times to decide the coin is fair. You model the coin flips as X1,â¦,Xnâ¼iidBer(p) where p is an unknown parameter, and formulate the hypothesis: H0: p=0.5
H1: pâ 0.5, and design the test Ï using the statistic Tn :

Ïn = 1(Tn>C)
where Tn = nââââ£â£X¯¯¯¯nâ0.5â£â£0.5(1â0.5 )âââââââââââ

If it is true that p=1/2, which of the following are true about Tn?
(Choose all that apply.)

a. Tn is a consistent estimator of the true parameter p=1/2.
b. limnâ[infinity]Tnâââânâ[infinity](d )|Z| where Zâ¼N(0,1) is a standard Gaussian.
c. Tn involves a shift and rescaling of the sample average so that as nâ[infinity], this random variable will converge in distribution.
d. The limiting distribution of Tn can be understood using computational software or tables.