Question

7.14 The table below shows the choices made by 119 players on the first turn of a Rock-Paper-Scissors game. Recall that rock beats scissors which beats paper which beats rock. A player gains an advantage in playing this game if there is evidence that the choices made on the first turn are not equally distributed among the three options. Use a goodness-of-fit test to see if there is evidence that any of the proportions are different from 1/3.

Frequencies for first turn in Rock-Paper-Scissors

Options Selected	Frequency
Rock	66
Paper	39
Scissors	14
Total	119

Answer 1

Ho: choice made on the first term are equally distributed among the three options

Ha:  choices made on the first turn are not equally distributed among the three options.

degree of freedom =categories-1=			2
for 0.05 level and 2 degree of freedom :rejection region =					5.991
applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
Rock	0.333	66.000	39.6667	4.18	17.482
Paper	0.333	39.000	39.6667	-0.11	0.011
Scissors	0.333	14.000	39.6667	-4.08	16.608
total	1.000	119	119		34.1008

test statistic X2 =

34.1008

since test statistic falls in rejection region we reject null hypothesis
we have sufficient evidence to conclude that choices made on the first turn are not equally distributed among the three options.