Dice After getting trounced by your little brother in achildren’s game, you suspect the die he gave you to rollmay be unfair. To check, you roll it 60 times, recording the number of times each face ap-pears. Do these results cast doubt on the die’s fairness?a) If the die is fair, how many timeswould you expect each face toshow?b) To see if these results are unusual, will you test goodness-of-fit, homo-geneity, or independence?c) State your hypotheses.d) Check the conditions.e) How many degrees of freedom are there?f) Find x2and the P-value.g) State your conclusion.
Dice After getting trounced by your little brother in achildren’s game, you suspect the die he gave you to rollmay be unfair. To check, you roll it 60 times, recording the number of times each face ap-pears. Do these results cast doubt on the die’s fairness?a) If the die is fair, how many timeswould you expect each face toshow?b) To see if these results are unusual, will you test goodness-of-fit, homo-geneity, or independence?c) State your hypotheses.d) Check the conditions.e) How many degrees of freedom are there?f) Find x2and the P-value.g) State your conclusion.
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 5ECP: How many permutations of the letters W, X, Y, and Z are possible?
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Question
Dice 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 60 times, recording
children’s game, you suspect the die he gave you to roll
may be unfair. To check, you roll it 60 times, recording
the number of times each face ap-
pears. Do these results cast doubt on
pears. Do these results cast doubt on
the die’s fairness?
a) If the die is fair, how many times
would you expect each face to
show?
b) To see if these results are unusual,
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, homo-
geneity, or independence?c) State your hypotheses.
d) Check the conditions.
e) How many degrees of freedom are there?
f) Find x2
and the P-value.
g) State your conclusion.
geneity, or independence?c) State your hypotheses.
d) Check the conditions.
e) How many degrees of freedom are there?
f) Find x2
and the P-value.
g) State your conclusion.
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