Question

Are steers and heifers equally distributed between angus and herefords

Case	Breed	Sex
1	hereford	Heifer
2	hereford	Heifer
3	hereford	Steer
4	Angus	Steer
5	Angus	Steer
6	hereford	Heifer
7	hereford	Heifer
8	hereford	Heifer
9	hereford	Steer
10	hereford	Steer
11	hereford	Heifer
12	hereford	Heifer
13	Angus	Steer
14	hereford	Heifer
15	Angus	Steer
16	hereford	Heifer
17	Angus	Steer
18	hereford	Heifer
19	Angus	Steer
20	Angus	Steer
21	Angus	Steer
22	Angus	steer
23	Angus	Steer
24	hereford	Steer
25	hereford	Steer
26	hereford	Steer
27	Angus	Steer
28	Angus	Heifer
29	hereford	Steer
30	Angus	Steer
31	hereford	Heifer
32	hereford	Heifer
33	Angus	Steer
34	hereford	Steer
35	hereford	Heifer
36	hereford	Heifer
37	Angus	Steer
38	Angus	Steer
39	Angus	Heifer
40	hereford	Steer
41	hereford	Heifer
42	Angus	Steer
43	Angus	Steer
44	hereford	Steer
45	hereford	Heifer
46	hereford	Heifer
47	hereford	Heifer
48	hereford	Heifer
49	hereford	Heifer
50	hereford	Heifer
51	Angus	Heifer
52	hereford	Steer
53	Angus	Steer
54	Angus	Steer
55	Angus	steer
56	Angus	Heifer
57	hereford	Heifer
58	Angus	steer
59	hereford	Steer
60	hereford	Heifer
61	hereford	Heifer
62	Angus	Heifer
63	hereford	Steer
64	Angus	Steer
65	hereford	Heifer
66	hereford	Heifer
67	hereford	Heifer
68	hereford	Heifer
69	hereford	Heifer
70	Angus	Steer
71	Angus	Steer
72	Angus	Steer
73	Angus	Steer
74	hereford	Heifer
75	hereford	Heifer
76	Angus	Steer
77	hereford	Heifer
78	hereford	Steer
79	Angus	Steer
80	hereford	Heifer
81	Angus	Steer
82	hereford	Steer
83	Angus	Heifer
84	hereford	Steer
85	hereford	Steer
86	hereford	Heifer
87	hereford	Steer
88	hereford	Heifer
89	hereford	Heifer
90	Angus	Steer
91	hereford	Heifer
92	Angus	Steer
93	hereford	Heifer
94	Angus	Heifer
95	Angus	Heifer
96	hereford	Heifer
97	hereford	Steer
98	hereford	Steer
99	Angus	Heifer
100	Angus	Steer

Answer 1

The problem can be modeled using chi square test of independence, where the null hypothesis states that -

steers and heifers are equally distributed between angus and herefords

And, alternate hypothesis states that -

steers and heifers are significantly differently distributed between angus and herefords

Simplifying the table -

	Steer	Heifer
Angus	32	9	41
Hereford	20	39	59
	52	48	100

	Steer (observed)	Steer (expected)	chi sq	Heifer (observed)	Heifer (expected)	chi sq	Total
Angus	32	21.32	5.35	9	19.68	5.8	41
Hereford	20	30.68	3.72	39	28.32	4.03	59
	52			48			100

Where, expected value = row total * column total / total

and, chi square value = (observed - expected)^2 / expected

combined chi square value = 18.9

Looking at the chi square table for 1 degree of freedom and value of 18.9, the p value is .000014.

(degree of freedom = (row -1) * (column -1)

The result is significant even at 0.0001 significance level.

Hence, we reject our null hypothesis.

steers and heifers are significantly differently distributed between angus and herefords