Question

You suspect that an unscrupulous employee at a casino has tampered with a die; that is, he is using a loaded die. In order to test this claim, you roll the die 200 times and obtain the following frequencies: (You may find it useful to reference the appropriate table: chi-square table or F table) Click here for the Excel Data File Category 1 2 3 4 5 6 Frequency 40 35 33 30 33 29 a. Choose the appropriate alternative hypothesis to test if the population proportions differ. All population proportions differ from 1/6. Not all population proportions are equal to 1/6.

b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)

Answer 1

(a)

H0:Null Hypothesis: All population proportions are equal to 1/6. (Claim)

HA:Alternative Hypothesis: Not all population proportions are equal to 1/6.

(b)

Test Statistic () is calculated as follows:

Observed (O)	Expected (E)	(O - E)2?E
40	200/6 = 33.3333	(40-33.3333)2/33.3333=1.3333
35	200/6 = 33.3333	(35-33.3333)2/33.3333=0.0833
33	200/6 = 33.3333	(33-33.3333)2/33.3333=0.0033
30	200/6 = 33.3333	(30-33.3333)2/33.3333=0.3333
33	200/6 = 33.3333	(33-33.3333)2/33.3333=0.0033
29	200/6 = 33.3333	(29-33.3333)2/33.3333=0.5633
Total = Test Statistic () =		2.320

the value of the test statistic. = 2.320

(c)

df = 6 - 1= 5

Take = 0.05

From Table, critical value of = 11.07

Since calculated value of = 2.320 is less than critical value of = 11.07, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data support the claim that all population proportions are equal to 1/6.