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 294 times and obtain the following frequencies: 2 58 3 57 4 40 54 54 31 (Use Table 3) Click here for the Excel Data File a. Choose the appropriate alternative hypothesis to test if the population proportions differ Not all population proportions are equal to 1/6 All population proportions differ from 1/6. b-1. Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places and your final answer to 2 decimal places.) Test statistic b-2. Approximate the p-value 0.050 p-value < 0.100 0.025 p-value < 0.050 p-value > 0.100 0.010 p-value < 0.025 p-value < 0.005 C. At the 1% significance level, can you conclude that the die is loaded? No since the p-value is more than a Yes since the p-value is less than a. Yes since the p-value is more than a No since the p-value is less than ?

Answer 1

a) not all population proportion are equal to 1/6

b-1)

applying chi square goodness of fit test:

		observed	Expected		Chi square
category	Probability(p)	Oi	Ei=total*p		R2i=(Oi-Ei)2/Ei
1	1/6	54.000	49.00		0.51
2	1/6	58.000	49.00		1.65
3	1/6	57.000	49.00		1.31
4	1/6	40.000	49.00		1.65
5	1/6	54.000	49.00		0.51
6	1/6	31.000	49.00		6.61
total	1	294	294		12.245

test statistic =12.24 ( please try 12.25 if this comes wrong)

b-2) 0.025 < p value <0.05

c)

No sine the p value is more than alpha