Question

The table below shows the choices made by 125 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 it there is evidence that any of the proportions are different from 1/3.

Option Selected	Frequency
Rock	66
Paper	44
Scissors	15
Total	125

Calculate the chi-square test statistic and the p-value and round your answer for the chi-square statistic to two decimal places, and your answer for the p-value to three decimal places.

x2=

p value=

Answer 1

The null and alternative hypothesis

H0: p1=p2=p3=1/3

Ha: At least one of the proportion is different from 1/3

Test statistic is

where Oi : observed frequency

Ei : expected frequency

Expected frequency calculation

Option selected	Ei
Rock	41.66667
Paper	41.66667
Scissor	41.66667
Total	125

Calculation of Chi square

	Oi	Ei	(Oi-Ei)^2/Ei
	66	41.6667	14.2106
	44	41.6667	0.1307
	15	41.6667	17.0667
total			31.4080

Thus

31.41

df = 3-1=2

P value =0.000

Since P value < 0.05

We reject H0

There is sufficient evidence to conclude that at least any of the proportions are different from 1/3

Note : Excel formula for P value "=CHISQ.DIST.RT(31.41,2)"