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 - 14 times, HT - 18 times, TH - 13 times, and TT - 34 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 Frequency = 14 + 18 + 13 + 34 = 79

As each of the above event should be equally likely, therefore the expected frequency for each of the outcomes mentioned should be (79/4) = 19.75

Therefore the chi square test statistic here is computed as:

1* = [ (0; – E:)! E;

$\chi^2 = \frac{(14 - 19.75)^2 + (18 - 19.75)^2 + (13 - 19.75)^2 + (34 - 19.75)^2}{19.75}$

x2 = 14.4177

Therefore 14.4177 is the test statistic value here.