Question

A coin is tossed 1000 times and 540 heads appear. At ΅= 0.05, test the claim that this is nota biased coin.

Answer 1

Solution:

Claim: The coin is not biased

Let p be the true proportion of heads.

So , the null and alternative hypothesis are

H₀ : p = 0.5 vs H₁ : p 0.5

Sample size n = 1000

x = 540

Let   be the sample proportion.

= x/n = 540/1000  = 0.540

The test statistic z is

z =    

=  (0.540 - 0.5)/[0.5*(1 - 0.5)/1000]

= 2.53

Test statistic z = 2.53

Now we find p value

sign in H1 indicates that the test is "Two Tailed"

p value = P(Z < -z) + P(Z > +z) = P(Z < -2.53) + P(Z > +2.53) = 0.0057 + 0.0057 = 0.0114

p value = 0.0114 is less than = 0.05

Reject H0 . There is sufficient evidence to warrant rejection of the claim that the coin is not biased.