Suppose you want to test how fair is the coin. You conduct the following experiment. You...

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?

Solutions

Expert Solution

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.

*** if you have any doubt regarding the problem ,please write it in the comment box...if satisfied,please UPVOTE.

orchestra answered 1 year ago

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