a coin was tossed 400 times and the head turned up 216 times. test the hypothesis that the coin is unbiased. given that Z at 5% level of significance is 1.96 please solve this and give me a detailed answer.
2007-01-07 19:20:53 · 1 answers · asked by Jagdeep g 1 in Science & Mathematics ➔ Mathematics
Our null hypothesis is that the coin is fair (p(Heads) = 0.5) and the alternative is that it is biased (p(Heads) <> 0.5). We need to find the probability of getting a result at least as extreme as the one we actually got, if the null hypothesis is correct.
Since we have 400 repeated boolean trials (each with 0.5 probability of success according to the null hypothesis), we can use the normal approximation to the binomial distribution. The mean is Np = 200 and the variance Npq = Np(1-p) = 100, so the standard deviation is 10.
P(|X-200| > 215.5) = P(|Z| > 1.55) = 2.P(Z > 1.55) = 2(0.0606) = 0.121 to 3 d.p. This represents weak evidence that the coin is fair.
2007-01-07 19:33:18 · answer #1 · answered by Scarlet Manuka 7 · 1⤊ 0⤋