Question

A four-sided die is rolled 90 times; the results are in the table below. Conduct a hypothesis test to determine if there is evidence that the die is unfair/weighted.

Face Value	Frequency
1	24
2	28
3	22
4	16

Which pair of hypotheses is correct?

A) Ho: The distribution is U(4).                  

      Ha: The distribution is not U(4).

B) Ho: The die is fair.                     

      Ha: The die is not fair.

C) Ho: The probability of each face is ¼.                 

Ha: At least one face has a different    

probability.

D) All of the above are correct.

Which type of test should be used for this data?

A) Z-test

B) T-test

C) χ2 -test       

Compute the test statistic, round to 3 decimals.

            Test Statistic= _________________________

Compute the p-value, round to 4 decimals (2 if you convert to %):

p-value= _________________________

Using a 5% significance level, which is the correct conclusion?

            A) The data is evidence the die is fair.

            B) The data is not evidence the die is not fair.

            C) The data is evidence the die is not fair.

Answer 1

1)D) All of the above are correct.

2)

C) χ2 -test     

3)

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	1/4	24	22.50	0.32	0.100
2	1/4	28	22.50	1.16	1.344
3	1/4	22	22.50	-0.11	0.011
4	1/4	16	22.50	-1.37	1.878
total	1.000	90	90		3.3333
test statistic X2 =		3.333

frm excel:

p value =

chidist(3.333,3) =

0.3430

since p value>0.05

  B) The data is not evidence the die is not fair.