A die is said to be fair if the probability of rolling the number i is pi = 1/6

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.

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

Round your answer to the nearest 0.01.

Flag this Question

Question 21 pts

Continue the previous problem.

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

Round your answer to the nearest 0.01.

Flag this Question

Question 31 pts

Continue the previous problem.

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.

Flag this Question

Question 41 pts

Continue the previous problem.

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.

Flag this Question

Question 51 pts

Continue the previous problem.

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

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

Explanation / Answer

11)

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

21)

applying chi square goodness of fit test:

test statistic =3.47

31)

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

41)

p value =0.63

51)

Yes

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

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.