Question

a coin tossed 4040 times. Out of 4040 we have 1992 heads. A student wants to test the coin is fair or not at a= .05. Carry out the test using the p-value approach.

Answer 1

Here' the answer to the question. please write back in case you've doubts.

Lets calculate the test statistic first.

Test-statistic = ?

pcap = x/n = 1992/4040 = 0.4931

p = probability of getting either side of a fair coin = .50

So, test-statistic
= (pcap - p)/sqrt(p*p'/n)
= (.4931-.50)/sqrt(.5*.5/4040)
= -0.877

Now, P(|z| > 0.877 ) = 0.3804, which is way more than .05

Decision: don't reject null hypothesis. In other words we don't have enough evidence to prove that the coin is not fair. Hence this coin is fair

Answer: Coin is fair