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

H₀ : p = 0.5

H_a : p 0.5

= x / n = 15 / 20 = 0.75

Test statistic = z

= - P₀ / [P_{0 *} (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 .