In 10000 independent tosses of a coin it landed heads 5400 t

In 10,000 independent tosses of a coin, it landed heads 5400 times. Is it reasonable to assume that the coin is not fair? Explain.

The test hypothesis:

Ho: p=0.5 (i.e. null hypothesis)

Ha: p not equal to 0.5 (i.e. alternative hypothesis)

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(5400/10000-0.5)/sqrt(0.5*0.5/10000)

It is a two-tailed test.

Assume that the significant level a=0.05

The critical values are Z(0.025) = -1.96 or 1.96 (from standard normal table)

The rejection regions are if Z<-1.96 or Z>1.96, we reject the null hypothesis.

Since Z=8 is larger than 1.96, we reject the null hypothesis.

So we can conclude that the coin is not fair