Question

A coin is tossed 225 times and shows heads 135 times. Is the coin fair ?

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Answer 1

here we have given,

n=225, and provbability of getting heads is ,

p^=135/225=0.6

• Null hypothesis H0: p= p0    coin is fair  
• Alternative Hypothesis H1: p≠ p0 : the coin is not fair

p0= 0.5 because the probability of getting head is 1/2.

test statistics :

where n is the sample size.

Decision Rule: Reject if |z| > 1.96. from the table at 0.05

here z>1.96, so we reject the null hypothesis and conclude that their coin is not fair.