Question

An experimenter flips a coin 100 times and gets 44 heads. Test the claim that the coin is fair against the two-sided claim that it is not fair at the level α=.01

Answer 1

Let 'P' denote the true proportion of heads obtained.

The null and alternate hypothesis are:

H0: $P=0.5$

Ha:

P +0.5

The test statistic is given by:

$Z=\frac{p-P}{\sqrt{\frac{P(1-P)}{n}}}=\frac{\frac{44}{100}-0.5}{\sqrt{\frac{ 0.5(1-0.5)}{100}}}=-1.20$

Since this is a two-tailed test, so the p-value is given by:

$\\2\times P(Z<-1.20)=2\times P(Z>1.20)=2\times [1-P(Z<1.20)]\\ \\ =2\times [1-0.88493]=0.23014$

Since p-value is greater than 0.01, so we do not have sufficient evidence to reject the null hypothesis H0.

Thus we cannot conclude that the coin isn't fair.