Suppose that a certain coin comes up heads with 70 probabili

Suppose that a certain coin comes up heads with 70% probability. A one- tailed z procedure with = .01 is used to test if the coin gives heads more than 50% of the time, based on 100 trials. What is the approximate probability that the test will correctly identify the coin as unfair?

Solution

Suppose we are given that X has a distribution and we want to carry out a hypothesis test on the mean, l, based upon a sample observation of 100

Suppose the hypotheses are:
H0: l >0.50
H1: l < 0.50

We want to test if it is \"reasonable\" for the observed value of 100 to have a coin identified as an unfair

P(X>0.50) = 0.70 (qs given in the question)

The probability is greater than 0.01, so there is more than a 1% chance that the coin will be identified as an unfair. We therefore reject the null hypothesis in favour of the alternative at the 1% level.

However, the probability is greater than 0.01, so we would not reject the null hypothesis in favour of the alternative at the 1% level.