Question

A die is rolled 120 times to see if it is fair. The table below shows the outcomes. Face Value 1 2 3 4 5 6 Observed Frequency 15 18 26 20 14 27 What can be concluded using a level of significance of 0.05?

H0: The distribution is uniform.

H1: The distribution is not uniform.

p-Value =

Conclusion: There is insufficient or There is evidence

Answer 1

Answer:

Given that:

A die is rolled 120 times to see if it is fair. The table below shows the outcomes.

Face Value 1 2 3 4 5 6

Observed Frequency 15 18 26 20 14 27

Chi square test for Goodness of fit
  
expected frequncy,E = expected proportions*total frequency

expected frequncy,E=1/6 *120

expected frequncy,E = 20

total frequency= 120

observed frequencey, O	expected frequency,E	(O-E)^2/E
15	20.00	1.250
18	20.00	0.200
26	20.00	1.800
20	20.00	0.000
14	20.00	1.800
27	20.00	2.450

chi square test statistic,

chi square test statistic,
  
level of significance, = 0.05

Degree of freedom=k-1

Degree of freedom = 6 -1

Degree of freedom = 5
  
P value = 0.1860 [ excel function: =chisq.dist.rt(test-stat,df) ]

Decision:

P value >α , Do not reject Ho

conclusion: there is not enough evidence to conclude that distributon is not uniform