Question

Can people tell the difference between a female nose and a male nose? Eight Caucasian males and eight Caucasian females posed for nose photos. The article states that none of the volunteers wore nose studs or had prominent nasal hair. Each person placed a black Lycra tube over his or her head in such a way that only the nose protruded through a hole in the material. Photos were then taken from three different angles: front view, three-quarter view, and profile. These photos were shown to a sample of undergraduate students. Each student in the sample was shown one of the nose photos and asked whether it was a photo of a male or a female; and the response was classified as either correct or incorrect. The accompanying table was constructed using summary values reported in the article. Is there evidence that the proportion of correct sex identifications differs for the three different nose views? Test the appropriate hypotheses using a .05 significance level. (Round your answer to two decimal places.)

Sex ID	View
	Front	Profile	Three-Quarter
Correct	29	26	28
Incorrect	11	14	12

χ² =  

P-value interval

p < 0.001

0.001 ≤ p < 0.01    

0.01 ≤ p < 0.05

0.05 ≤ p < 0.10

p ≥ 0.10

Answer 1

Applying chi square test of independence:

Expected	Ei=row total*column total/grand total	Front	Profile	three quarter	Total
	Correct	27.6667	27.6667	27.6667	83
	Incorrect	12.3333	12.3333	12.3333	37
	total	40	40	40	120
chi square    χ2	=(Oi-Ei)2/Ei	Front	Profile	three quarter	Total
	Correct	0.064	0.100	0.004	0.1687
	Incorrect	0.144	0.225	0.009	0.3784
	total	0.2084	0.3256	0.0130	0.5471
test statistic X2 =		0.55

p ≥ 0.10

Fail to reject the null hypothesis