Question

5. You’re competing in the rock paper scissors international tournament. Use the following information to determine whether your semifinal opponent over-represents certain choices (?=0.05). Show all relevant values behind your decision.

6. 	Frequency
   Rock	85
   Paper	110
   Scissors	105
   Total	300

Answer 1

null Hypothesis:Ho All choices occur with equal probability.

Alternate Hypothesis:Ha: Not all choices occur with equal probability.

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	85.000	100.0000	-1.50	2.250
Paper	0.333	110.000	100.0000	1.00	1.000
Scissors	0.333	105.000	100.0000	0.50	0.250
total	1.000	300	300		3.5000

test statistic X2 =

3.5000

since test statistic does not falls in rejection region we fail to reject null hypothesis
we do not have have sufficient evidence to conclude that semifinal opponent over-represents certain choices