Question

Clare and Bonny are flipping a coin, if it comes up heads Bonny pays Claire $5 and for tails Clare pays Bonny $5. After playing this game all day Bonny notices that Clare has won 59 of the 100 rounds. Should Bonny be suspicious of Clare's coin? Why or why not

Answer 1

In this problem a coin tossing game has been performed between Clare and Bonny. On each throw of coin, Claire wins if head appears, otherwise Bonny wins.

After the game it is observed that Claire wins more. That is among 100 tosses Head appears 59 times

We need to test whether coin is unbiased or not.

Let, p=probability of the head at a thrown of this coin.

To test,

H0: p=0.5

Vs

H1: p>0.5

Test statistic,

Where p^=59/100=0.59

p=0.5

n=100

We will reject H0 if T>=critical point

By calculation, T=1.8

We take significance level =0.05

So the critical point is

Here we get T >1.64. So we will reject H0 and claim that the coin of Clare was not biased at 95% confidence.