A company wishes to test whether the proportion of female ma

A company wishes to test whether the proportion of female managers is the same as the proportion of male managers. The following table provides data for a sample of employees. Females Males Number of managers 18 23 Sample size 45 75 Formulate the null and the alternative hypotheses to determine if the proportion of female managers is the same as the proportion of male managers. (Points : 1) H0: pfemales - pmales 0 H1: pfemales - pmales = 0 H0: pfemales - pmales = 0 H1: pfemales - pmales > 0 H0: pfemales - pmales = 0 H1: pfemales - pmales 0 H0: pfemales - pmales = 0 H1: pfemales - pmales < 0

Solution

H0: pfemales - pmales = 0 H1: pfemales - pmales 0

Pfemale = 18 / 45 = 0.4

P male = 23 / 75 = 0.31

P = 18+23 / 45+75 = 0.34

error = srqt ( 0.34 * 0.66 * ( 1/45 + 1/75 )

error = 0.089

Z = 0.4-0.31 / 0.089

Z = 1.01

for alpha = 0.05

alpha / 2 = 0.025

critical value : 1.96

conclusion we dont reject Ho because Z < 1.96

the proportion of female managers is the same as the proportion of male managers.