Question

(a) One day, upon tossing a single die 180 times, I got: 32 ones, 28 twos, 35 threes, 36 fours, 29 fives, and 20 sixes. Computer χ2 and find P for this experiment.

(b) Another day, upon tossing a single die 120 times, I got: 12 ones, 26 twos, 20 threes, 21 fours, 15 fives, and 26 sixes. Computer χ2 and find P for this experiment.

(c). Now, computer the pooled χ2 using the combined degrees of freedom, and find the pooled P-values

Answer 1

(a) Here χ2 =

Roll	Frequency	Expected	χ2
1	32	30	0.133
2	28	30	0.133
3	35	30	0.833
4	36	30	1.2
5	29	30	0.033
6	20	30	3.333
Total	180	180	5.667

Here degree of freedom = dF = 6 -1 = 5

P - value = CHIINV(5.667, 5) = 0.3400

(b) Now here

Roll	Frequency	Expected	χ2
1	12	20	3.2
2	26	20	1.8
3	20	20	0
4	21	20	0.05
5	15	20	1.25
6	26	20	1.8
Total	120	120	8.1

χ2 = 8.1

dF = 6 -1 = 5

P - value = CHIINV(8.1, 5) = 0.1508

(c) Now adding

Here using pooled chi-square we get following table

Roll	Frequency	Expected	χ2
1	44	50	0.72
2	54	50	0.32
3	55	50	0.5
4	57	50	0.98
5	44	50	0.72
6	46	50	0.32
Total	300	300	3.56

χ2 = 3.56

dF = 6 -1 = 5

P - value = CHIINV(3.56, 5) = 0.6143