Question

A die is said to be fair if the probability of rolling the number i is pi = 1/6 for i = 1, ..., 6. One student rolls a die 180 times with the following outcome.

number	1	2	3	4	5	6
frequency	38	27	33	27	28	27

What is the expected frequency for rolling 3 if the die is fair.

Round your answer to the nearest 0.01.

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Question 21 pts

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Calculate the test statistic X2 for testing H0: the die is fair.

Round your answer to the nearest 0.01.

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Question 31 pts

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What is the number of degreese of freedom for the test statistic X2 for testing H0: the die is fair.

Round your answer to the nearest 0.01.

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Question 41 pts

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What is the p-value for the test statistic X2 for testing H0: the die is fair.

Round your answer to the nearest 0.01.

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Question 51 pts

Continue the previous problem.

Based on the p-value, is this die fair?

Yes

Cannot tell.

No

Answer 1

11)

expected frequency for rolling 3 if the die is fair =np=180*(1/6)=30

21)

applying chi square goodness of fit test:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
1	1/6	38.000	30.000		2.133
2	1/6	27.000	30.000		0.300
3	1/6	33.000	30.000		0.300
4	1/6	27.000	30.000		0.300
5	1/6	28.000	30.000		0.133
6	1/6	27.000	30.000		0.300
total	1.000	180	180		3.467

test statistic =3.47

31)

degree of freedom =categories-1=6-1=5

41)

p value =0.63

51)

Yes