Question

In a random sample of​ males, it was found that

24

write with their left hands and

207

do not. In a random sample of​ females, it was found that

57

write with their left hands and

465

do not. Use a

0.05

significance level to test the claim that the rate of​ left-handedness among males is less than that among females.

Identify the test statistic.

z=

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-value=

​(Round to three decimal places as​ needed.)

Answer 1

To Test :-

H0 :- P1 = P2
H1 :- P1 < P2

p̂1 = 24 / 231 = 0.1039
p̂2 = 57 / 522 = 0.1092

Test Statistic :-
Z = ( p̂1 - p̂2 ) / √(p̂ * q̂ * (1/n1 + 1/n2) ) )
p̂ is the pooled estimate of the proportion P
p̂ = ( x1 + x2) / ( n1 + n2)
p̂ = ( 24 + 57 ) / ( 231 + 522 )
p̂ = 0.1076
q̂ = 1 - p̂ = 0.8924
Z = ( 0.1039 - 0.1092) / √( 0.1076 * 0.8924 * (1/231 + 1/522) )
Z = -0.22

P value = P ( Z < -0.22 ) = 0.414