A six-sided die is rolled 120 times. Fill in the expected frequency column. Then

Question

A six-sided die is rolled 120 times. Fill in the expected frequency column. Then, conduct a hypothesis test at the 5% level to determine if the die is fair. The data below are the result of the 120 rolls. (Enter exact numbers as integers, fractions, or decimals.)

Part (a)

State the null hypothesis. Choose 1 or 2

1. The data fit the distribution for a fair six-sided die.

2. The data do not fit the distribution for a fair six-sided die.    

Part (b)

State the alternative hypothesis. Choose 1 or 2

1. The data fit the distribution for a fair six-sided die.

2. The data do not fit the distribution for a fair six-sided die.    

Part (c)

What are the degrees of freedom? (Enter an exact number as an integer, fraction, or decimal.)

Part (d)

State the distribution to use for the test.

t5

?26

OR

t6

?25

Part (e)

What is the test statistic? (Round your answer to two decimal places.)  

_______

What is the p-value? (Round your answer to four decimal places.)
________

Face Value Frequency Expected Frequency 1 14 ? 2 33 ? 3 15 ? 4 14 ? 5 30 ? 6 14 ?

Explanation / Answer

a)

null hypothesis. The data fit the distribution for a fair six-sided die.

b)

alternative hypothesis: 2. The data do not fit the distribution for a fair six-sided die

c)

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

d)

?25

e)

applying chi square test of goodness of fit:

  test statistic =20.10

p value =0.0012

observed Expected Chi square category Probability(p) Oi Ei=total*p R2i=(Oi-Ei)2/Ei 1 1/6 14.000 20.00 1.800 2 1/6 33.000 20.00 8.450 3 1/6 15.000 20.00 1.250 4 1/6 14.000 20.00 1.800 5 1/6 30.000 20.00 5.000 6 1/6 14.000 20.00 1.800 total 1 120 120 20.100

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