Question

Suppose you want to test how fair is the coin. You conduct the following experiment. You flip the 2 coins multiple times and observe HH - 34 times, HT - 15 times, TH - 27 times, and TT - 14 times. What is the Test Statistics to test the Null Hypothesis that the coin is fair against the alternative hypothesis that the coin is unfair?

Answer 1

If the coin is fair, then all the combination are equally likely. In other words, P(HH) = P(HT) = P(TH) = P(TT) = 1/4 = 0.25

The null and alternative hypotheses are as follows:

H₀​: p_1​ = 0.25, p₂ ​= 0.25, p₃​ = 0.25, p₄​ = 0.25

H_a​: Some of the population proportions differ from the values stated in the null hypothesis

where,

p_1​ = Population proportion of HH

p_2​ = Population proportion of HT

p₃ = Population proportion of TH

p_4​ = Population proportion of TT