After getting trounced by your little brother in a childrens

After getting trounced by your little brother in a children\'s game, you suspect the die he gave you to roll may be unfair. To check, you roll it 96 times, recording the number of times each face appears. Do these results cast doubt on the die\'s fairness?

Face    Count    Face    Count

1          10          4          8

2          20         5           12

3          14         6           32

a) If the die is fair, how many times would you expect each face to show?

b) To see if these results are unusual, will you test goodness-of-fit, homogeneity, or independence?

c) State your hypotheses. Choose the correct answer below.

d) Check the conditions. Is the counted data condition met? Is the randomization condition met? Is the expected cell frequency condition met?

e) How many degrees of freedom are there?

f) Find chi squared and the P-value.

g) State your conclusion. Choose the correct answer below.

Solution

a) expected for each face

we have in total 96 and we divided by 6 and that will be our expected value for each face

expected value : 16

b) homogeneity

c)

Ho : p1 = p2 = p3 = .... = p6

H1 : there are different

D)

Is the counted data condition met? YES

Is the randomization condition met? YES

Is the expected cell frequency condition met? YES

e)   6-1 =5

f) X^2 = 24.5

P VALUE WILL BE : 0.00001

CONCLUSION

WE REJECT Ho