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 - 23 times, HT - 24 times, TH - 37 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

the all possible outcomes when you toss 2 fair coins = { HH,HT,TH,TT}

if the coin is fair,

then the possobility of all the 4 outcomes will be equal ,i.e, 1/4 = 0.25

hypothesis:-

(i.e, the coin is fair)

the necessary calculation table :-

outcomes	observed	expected
HH	23	118*0.25 = 29.5	(23-29.5)2/29.5 = 1.43220
HT	24	29.5	1.02542
TH	37	29.5	1.90678
TT	24	29.5	0.68644
	sum = 118		sum = 5.05084

test statistic be:-

df = (4-1) = 3

p value = 0.1681

[ in any blank cell of excel type =CHISQ.DIST.RT(5.05084,3) ]

decision:-

p value = 0.1681 > 0.05 (alpha)

we fail to reject the null hypothesis. There is enough evidence to claim the coin to be fair.

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