Question

Judy wants to test whether a coin is fair or not. Suppose she observes 477 heads in 900 tosses. Perform an appropriate p-value test using a 10% level of significance, and state your decision and conclusion.

Answer 1

H0: p = 0.50 , Ha: p 0.5

Sample proportion = 477 / 500 = 0.53

Test statistics

z = - p / sqrt(p(1-p) / n)

= 0.53 - 0.50 / sqrt( 0.50 * 0.50 / 900)

= 1.8

This is test statistics value.

p-value = 2 * P( Z > z) (2 is multiplied to probability since this is two tailed test)

= 2 * P (Z > 1.8)

= 2 * ( 1 - P( Z < 1.8) )

= 2 * ( 1 - 0.9641 )

= 0.0718

This is p-value for the test.

Since p-value < 0.10 significance level, we have sufficient evidence to reject H0.

We conclude at 0.10 level that we have enough evidence to support the claim that coin is not fair.