Question

I flipped a coin 49 times and got heads only 18 times. I feel like the coin is biased. I run a 1 sample z test proportion with the null hypothesis set to .5 (50%) to represent a fair coin.

What's the p-value of the test?

Would you reject the null hypothesis or fail to reject the null hypothesis?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.5

H_a : p 0.5

n = 49

x = 18

= x / n = 18 / 49 = 0.3673

P₀ = 0.5

1 - P₀ = 1 - 0.5 = 0.5

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.3673 - 0.5 / [(0.5 * 0.5) / 49]

= -1.857

Test statistic = -1.857

P(z < -1.857) = 0.0317

P-value = 2 * P(z < -1.857) = 2 * 0.0317 = 0.0634

= 0.05

P-value >

Fail to reject the null hypothesis .