Question

1. Bob’s Lucky Golden Eagle, a $100 gold piece, when flipped 100 times gives 75 heads and 25 tails. Test to see if there is a significant difference. However, Bob wants to be 99% certain that his coin is not biased. For all questions report the null and alternate hypotheses. State if it is a one or two-tailed test. State the alpha level, the critical value, type of Chi Square and degrees of freedom.

Answer 1

We are testing,

H0: The coin is unbiased

vs H1: The coin is biased

For the test we will use a Chi square test of Independence.

Now, If a coin is flipped once Probability of getting heads= 0.5

So out of 100 flips, we expect 50 heads and 50 tails.

Observed Expected

Heads 75. 50

Tails 25. 50

Now, Chi square test statistic:

= (75-50)^2/50 + (25-50)^2/50

= 25

Df = (r-1)(c-1) = (2-1)*(2-1) = 1

If Bob wants to be 99% certain, them alpha level is 0.01

So, Critical value from chi square tables is:

Chi square 0.01,1 = 6.635

Since the test statistic > critical value, we have sufficient evidence to reject H0 at the 99% confidence level and conclude that yes, the coin is biased.