Question

4. A sociologist wants to show that the food you eat actually changes your perception of how other people are feeling. She gathered 1000 volunteers, and randomly selected what food they would eat. Then she asked them to look at a photograph (of a person showing no emotion) and asked them to mark what emotion they thought the person was experiencing. The data is shown below. Test at the 1% significance level if the food they ate is related to the emotion chosen. Sad 30 Sleepy 39 160 Chocolate Oranges Breadstick Salad Steak Happy 22 25 33 31 11 122 Angry 16 32 29 46 8 131 Surprised 9 8 11 21 6 Scared 4 4 65 25 102 12 248 32 65 7 182 181 98 8 I 363 52 1000

Answer 1

Chi-square Contingency Table Test for Independence

			Col 1	Col 2	Col 3	Col 4	Col 5	Col 6	Total
	Row 1	Observed	22	16	30	9	39	44	160
		Expected	19.52	20.96	29.12	8.80	41.92	39.68	160.00
		O - E	2.48	-4.96	0.88	0.20	-2.92	4.32	0.00
		(O - E)² / E	0.32	1.17	0.03	0.00	0.20	0.47	2.19
	Row 2	Observed	25	32	48	8	66	65	244
		Expected	29.77	31.96	44.41	13.42	63.93	60.51	244.00
		O - E	-4.77	0.04	3.59	-5.42	2.07	4.49	0.00
		(O - E)² / E	0.76	0.00	0.29	2.19	0.07	0.33	3.64
	Row 3	Observed	33	29	32	11	51	25	181
		Expected	22.08	23.71	32.94	9.96	47.42	44.89	181.00
		O - E	10.92	5.29	-0.94	1.05	3.58	-19.89	0.00
		(O - E)² / E	5.40	1.18	0.03	0.11	0.27	8.81	15.80
	Row 4	Observed	31	46	65	21	98	102	363
		Expected	44.29	47.55	66.07	19.97	95.11	90.02	363.00
		O - E	-13.29	-1.55	-1.07	1.04	2.89	11.98	0.00
		(O - E)² / E	3.99	0.05	0.02	0.05	0.09	1.59	5.79
	Row 5	Observed	11	8	7	6	8	12	52
		Expected	6.34	6.81	9.46	2.86	13.62	12.90	52.00
		O - E	4.66	1.19	-2.46	3.14	-5.62	-0.90	0.00
		(O - E)² / E	3.42	0.21	0.64	3.45	2.32	0.06	10.10
	Total	Observed	122	131	182	55	262	248	1000
		Expected	122.00	131.00	182.00	55.00	262.00	248.00	1000.00
		O - E	0.00	0.00	0.00	0.00	0.00	0.00	0.00
		(O - E)² / E	13.88	2.61	1.00	5.80	2.95	11.27	37.52

set up null vs alternative as
null, Ho: no relation b/w food they eat and emotion chosen
alternative, H1: exists a relation b/w food they eat and emotion chosen
level of significance, alpha = 0.01
from standard normal table, chi square value at right tailed, ᴪ^2 alpha/2 =44.3141
since our test is right tailed,reject Ho when ᴪ^2 o > 44.3141
we use test statistic ᴪ^2 o = Σ(Oi-Ei)^2/Ei
from the table , ᴪ^2 o = 37.52
critical value
the value of |ᴪ^2 alpha| at los 0.01 with d.f (r-1)(c-1)= ( 6 -1 ) * ( 6 - 1 ) = 5 * 5 = 25 is 44.3141
we got | ᴪ^2| =37.52   & | ᴪ^2 alpha | =44.3141
make decision
hence value of | ᴪ^2 o | < | ᴪ^2 alpha| and here we failed to reject Ho
we claim that no relation b/w food they eat and emotion chosen