Question

A die is rolled 120 times to see if it is fair. The table below shows the frequencies for each of the six possible outcomes. Use a level of significance of a=0.10. a. Complete the rest of the table by filling in the expected frequencies (enter your answers in fraction form) Frequency of Dice Values Outcome Frequency Expected Frequency aw- b. What is the correct statistical test to use? Select an answer c. What are the null and alternative hypotheses? Ho: The die rolls are dependent The distribution of die rolls is uniform The distribution of die rolls is not uniform The die rolls are independent

Answer 1

a)

		observed	Expected
category		Oi	Ei=total*p
1		23.000	20.000
2		18.000	20.000
3		25.000	20.000
4		26.000	20.000
5		13.000	20.000
6		15.000	20.000
total		120	120

b)chi square goodness of fit

c) Ho: the distribution..is uniform

H1: the distribution..is not uniform

d)

degree of freedom =categories-1=

5

e)

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
1	0.167	23.000	20.000	0.67	0.450
2	0.167	18.000	20.000	-0.45	0.200
3	0.167	25.000	20.000	1.12	1.250
4	0.167	26.000	20.000	1.34	1.800
5	0.167	13.000	20.000	-1.57	2.450
6	0.167	15.000	20.000	-1.12	1.250
total	1.000	120	120		7.400

test statistic X2 =

7.400

f)

p value =

0.1926

g)

greater than

h) fail to reject

i) there is insuffiicient.......is not uniform