A sequence of heads(H) and tails (T) in tossing of a coin 16 times are given below HTTTHTHTHHTHTTHH count the number of runs and also test whether the heads and the tails occur in a random order alpha =0.05
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Expert's answer
2021-08-05T13:48:48-0400
For the given sequence, the sample size n=16, number of heads n1=8, number of tails n2=8.
(H)(TTT)(H)(T)(H)(T)(HH)(T)(H)(TT)(HH)
number of runs of H,R1=6
number of runs of T,R2=5
So that number of runs is R=R1+R2=6+5=11.
H0: the sequence was produced in a random manner.
H1: the sequence was not produced in a random manner.
μ=n1+n22n1n2+1=8+82(8)(8)+1=9
s2=(n1+n2)2(n1+n2−1)2n1n2(2n1n2−n1−n2)
=(8+8)2(8+8−1)2(8)(8)(2(8)(8)−8−8)=1556
z=sR−μ=155611−9≈1.0351
For α=0.05,zc=1.96.
Since z=1.0351<1.96=zc, we accept H0. It means that the heads and tails occur in random order or it can be said that the coin is unbiased at the α=0.0 significance level.
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