Question

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.

Answer #1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H_{0} : p = 0.5

H_{a} : p
0.5

= x / n = 15 / 20 = 0.75

Test statistic = z

=
- P_{0} / [P_{0
*} (1 - P_{0} ) / 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 .

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