Question

Suppose that you tossed a coin 1000 times in which 560 of the tosses were heads while 440 were tails. Can we reasonably say that the coin is fair? Justify your answer. Hint: use the concept of p-values. To evaluate the resulting probability, use an approximation by way of the CLT. Why does this offer a good approximation? Use a z-table or R to evaluate the N(0,1) cdf.

Answer 1

Let P be the true proportion for number of heads.

The null and alternate hypothesis are:

H0: i.e. coin is fair

Ha: i.e. coin isn't fair

Using CLT, we know

The test statistic value is given by:

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

Since p-value is less than 0.05, so we have sufficient evidence to reject the null hypothesis
H0 at 5% level of significance.

Thus we can say that the coin isn't fair.