Question

Two successive flips of a fair coin is called a trial. 100 trials are run with

a particular coin; on 22 of the trials, the coin comes up “heads” both

times; on 60 of the trials the coin comes up once a “head” and once a

“tail”; and on the remaining trials, it comes up “tails” for both flips. Is this

sufficient evidence ( = : 05) to reject the notion that the coin (and the

flipping process) is a fair one?

(Hint: chi sq)

Answer 1

H0: Null Hypothesis: The coin is fair one

HA: Alternative Hypothesis: The coin is not fair one.

Observd Frequencies:

x           O

HH           22

HT, TH      60

TT             18

Under the Assumption of H0, the expected frequencies are:

x                 E

HH               25

Ht, TH           50

TT                 25

Chi square Table is formed as follows:

O	E	(O -E)2/E
22	25	0.36
60	50	2
18	25	1.96
Total = =		4.32

ndf = 3 - 1 = 2

= 0.05

From Table, critical value of = 5.9915

Since the claculated value of =4.32 is less than critical value of = 5.9915, the difference is not significant. Fail to reject null hypothesis. There is no sufficient evidence to reject the notion that the coin (and the lipping process) is a fair one.