Question

4. Sally Smith believes that she has been passed over for promotion because of her gender. She has requested the Human Resources Department of her company to investigate. They have taken a random sample of personnel who have applied for promotion over the last two years and classified them by gender and whether or not they were promoted. The results of the study are shown below: Male Female Promoted 80 45 Not Promoted 2 0 25. At an alpha level of 0.05 are promotions independent of gender or is there a relationship?

Make sure that each question has a set of hypotheses, work showing how you got your calculated F or chi square value, and your decision.

Answer 1

Observed Frequencies
	Promoted	Not Promoted	Total
Male	80	20	100
Female	45	25	70
Total	125	45	170
Expected Frequencies
	Promoted	Not Promoted	Total
Male	125 * 100 / 170 = 73.5294	45 * 100 / 170 = 26.4706	100
Female	125 * 70 / 170 = 51.4706	45 * 70 / 170 = 18.5294	70
Total	125	45	170
	(fo-fe)²/fe
Male	(80 - 73.5294)²/73.5294 = 0.5694	(20 - 26.4706)²/26.4706 = 1.5817
Female	(45 - 51.4706)²/51.4706 = 0.8134	(25 - 18.5294)²/18.5294 = 2.2596

Null and Alternative hypothesis:        

Ho: Factors are independent.  

H1: Factor are dependent.  

Test statistic:  

χ² = ∑ ((fo-fe)²/fe) = 5.2241

df = (r-1)(c-1) = 1

p-value:  

p-value = CHISQ.DIST.RT(5.2241, 1) = 0.0223  

Decision:  

p-value < α, Reject the null hypothesis.  

There is enough evidence to conclude that there is a relationship between gender and promotions.