Question

A statistics student reported getting 9207 heads and 8743 tails out of 17950 coin tosses. is this evidence that the coin is fair? coclysion at the 1percent level

Answer 1

for a coin to be fair ; proportion of head should be 0.5.

null Hypothesis:              Ho:   p=		0.500
alternate Hypothesis:    Ha: p ≠		0.500

for 0.01 level and two tailed test , critical z=			2.576	(from excel:normsinv(0.005)
Decision rule :   reject Ho if absolute value of test statistic |z|>2.576

sample success x   =		9207
sample size          n    =		17950
std error σp =√(p*(1-p)/n) =		0.0037
sample prop p̂ = x/n=9207/17950=		0.5129
z =(p̂-p)/σp=(0.513-0.5)/0.004=		3.46

since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence at 0.01 level of significance to conclude that coin is not fair