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 :

Given that,

= 0.5

1 - = 0.5

n = 20

x = 15

Level of significance = = 0.05

Point estimate = sample proportion = = x / n = 0.75

This a two tailed test.

A)

Ho: p = 0.5

Ha: p 0.5

Test statistics

z = ( - ) / *(1-) / n

= ( 0.75 - 0.5) / (0.5*0.5) / 20

= 2.24

P-value = 2*P(Z>z)

= 2*(1 - P(Z <z ))

= 2*(1- P(Z < 2.24))

= 2*( 1 - 0.9875)

= 2*0.0125

= 0.0250

The p-value is p = 0.0250, and since p = 0.0250 < 0.05, it is concluded that the null hypothesis is rejected.

Conclusion:

It is concluded that the null hypothesis is rejected, Therefore there is enough evidence to claim that the probability of flipping

heads or tails different than  0.5. at 0.05 significance level.