Question

The employment status of working students in Urdaneta City is below. Is there any difference in the proportion of employed in males and females? At 0.05 level of significance.
GENDER
EMPLOYMENT STATUS

EMPLOYED
UNEMPLOYED

MALES
280
25

FEMALES
250
77

TOTAL
530
102

Answer 1

$n_1=280,\;n_2=250.$

$p_1=\frac{25}{280}=0.0893, \;p_2=\frac{77}{250}=0.308,\;p_0=\frac{102}{530}=0.1925.$

Null hypothesis $H_0: \pi_1=\pi_2.$

Alternative hypothesis $H_a: \pi_1\ne\pi_2.$

Test statistic: $z=\frac{p_1-p_2}{\sqrt{p_0(1-p_0)(\frac{1}{n_1}+\frac{1}{n_2})}}=-6.38.$

P-value: $p=2P(Z<-6.38)<0.0001.$

Since the P-value is less than 0.05, reject the null hypothesis.