Question

Rock-Paper-Scissors

The table below shows the choices made by 122 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	65
Paper	43
Scissors	14
Total	122

Table 1 Frequencies for first turn in Rock-Paper-Scissors

Calculate the chi-square test statistic and the p-value.

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

χ 2 =

p-value =

Answer 1

hypothesis:-

all the proportions are equal to 1/3

at least one of the proportions are different from 1/3

the necessary calculation table:-

category	observed	expected
rock	65	122*1/3 = 40.6667	(65-40.6667)2/40.6667= 14.5601
paper	43	40.6667	0.1339
scissor	14	40.6667	17.4863
	sum=122		sum = 32.1803

the test statistic be:-

df = (3-1) = 2

the p value is :-

[ in any blank cell of excel type =CHISQ.DIST.RT(32.18,2) ]

decision:-

p value = 0.000 < 0.05 (Alpha)

we reject the null hypothesis. There is sufficient  evidence that any of the proportions are different from 1/3.

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