Question

There are 1000 students in the school of Engeering and Natural resources out of 20,000 in the whole coppebelt univesity. 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

Null hypothesis Ho: $p_1=p_2$

Alternative hypothesis Ha: $p_1\ne p_2$

Pooled proportion: $\hat p=\frac{200+1000}{1000+20000}=0.057.$

Test statistic: $z=\frac{\frac{200}{1000}-\frac{1000}{20000}}{\sqrt{0.057(1-0.057)(\frac{1}{1000}+\frac{1}{20000})}}=19.94.$

P-value: $p=2P(Z>19.94)<0.0001.$

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

There is a statistical significant difference between the proportions of smokers in the school and the university.