Question

Jared flips a single coin 800 times and counts 442 heads. He wonder if his coin is fair. Give 3 different arguments to help Jared out.

Answer 1

1)First we are going to check whether probability of head=probability of tail=0.5 fits the data well or not through goodness of fit test.

since p-value<0.05, we reject to conclude that the coin is fair.

2)Here we are considering n=800 trial and occurrence of a head is a success. Now we are to test whether probability of a success is 0.5 or not through exact binomial test.

since p-value<0.05, here also we reject to conclude that the coin is fair.

3)since n is quite large, we are going to test the same after applying CLT through single large sample proportion test.