Answer to Question #180664 in Statistics and Probability for EUGINE HAWEZA

Question

 There are 1000 students in the school of Engineering and Natural resources out of 20,000 in the whole Copperbelt university. In the study 200 were found to be smokers in the school and 1000 in the whole university. Is there a statistical significant difference between the proportions of smokers in the school and the university

Answer 1

This is a 2 sample proportion

p₁=0.2

p₂=0.05

$z=\dfrac{(p_1-p_2)} {\sqrt{phat \times(\frac{1}{n_1}+\frac{1}{n_2})}} =\dfrac{0.15} {\sqrt{phat \times(\frac{1}{1000}+\frac{1}{20000})}}$,

where phat is the pooled proportion of 0.057.

z=19.4

This is highly significant, given the large sample size and the large difference in proportions.