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 - 33 times, HT - 29 times, TH - 24 times, and TT - 26 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

Total trials = 33 + 29 + 24 + 26 = 112

Now the probabilities for different outcomes here are computed as:
P(HH) = 0.5*0.5 = 0.25
P(HT) = 0.5*0.5 = 0.25
P(TH) = 0.25, and P(TT) = 0.25

Therefore the expected frequency for each type of outcome here is computed as:
= 0.25*112 = 28

The chi square test statistic here is computed as:

Therefore 1.6429 is the required chi square test statistic value here.