Question

# Your friend claims he has a fair coin; that is, the probability of ﬂipping heads or...

Your friend claims he has a fair coin; that is, the probability of ﬂipping heads or tails is equal to 0.5. You believe the coin is weighted. Suppose a coin toss turns up 15 heads out of 20 trials. At α = 0.05, can we conclude that the coin is fair (i.e., the probability of ﬂipping heads is 0.5)? You may use the traditional method or P-value method.

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.5

Ha : p 0.5 = x / n = 15 / 20 = 0.75

Test statistic = z

= - P0 / [ P0 * (1 - P0 ) / n]

= 05 - 0.75/ [ (0.5 * 0.5) / 20]

= 2.37

P(z > 2.37) = 1 - P(z < 2.37) = 0.0095

P-value = 0.019 = 0.05

P-value < Reject the null hypothesis .

There is sufficient evidence to suggest that the probability of ﬂipping heads or tails is equal to 0.5 .

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