Question

The number of men and women among professors two academic areas (Science or Humanities) from a simple random sample of small colleges were counted, and the results are shown in the table below.

	Science	Humanities
Men	28	32
Women	12	28

Use the ?=0.01α=0.01 level of significance to determine whether or not the relationship between sex and academic area is statistically significant.

(a) ?2=χ2=

(b) Magic number =

(c) Is the relationship between sex and academic area statistically significant?

A. Yes
B. No

Answer 1

Solution: o Given that Science Total Humo nities men a - 28 b=32 60 atb Women d:28 40 ctd C-12 60 Total 100 EN ho brd a&C tevel of significance d-0101 @ Test statistics (ad-bc) 2 (a+b) (c+d)(Q+c)(6+d) (784-384)** 100 GO * no #40 ²60 160000 * 100 5760000 16000000 5760000

2 x² 2:7778 b Magical number: Degree of foeedom df = (0-1)(C-1) - (2-1)(2-1) =(1) (1) df = 1 2 xioul C - 6.635 Thug, magical numbeo 6:635 © 2 Хc 7 x 61635 7 2,7778 not conclusion :- we do not reject the null hypothesis at oor level of significance. There is sufficient evidence that seo and academic not independent.ie Plausible that and academic 9809 are independent. NO it is avea ade sex