Question

if you think a coin is biased, when you toss it 100 times and it results more tails than it should. Atleast how many tails do you need to determine the coin in fact is biased?

Answer 1

Null hypothesis: H0: Proportion of tails, P = 0.50

Alternate hypothesis: Ha: P not = 0.50

We know that the sample size is 100.

We also know that the number of tails is more than the optimal level. Hence the rejection would be on the right tail.

Assuming that we are using a level of significance of 5%. Thus, the Z critical value is 1.96.

We know that:

Z= (p-P) / sqrt (P*(1-p)/n)

1.96= (p-0.50) / sqrt(0.25/100)

1.96= (p-0.50) / 0.05

p-0.50= 0.098

p= 0.598

Thus the cutoff value for us to reject the null is 59.8%. Thus, at 5% significance, for a 2 tailed test, we need at least 60 tails to determine that the coin is biased.

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