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.)

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

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.)
________

Answer 1

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:

		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

  test statistic =20.10

p value =0.0012