In a survey conducted in 2003, the counts who smoked were 48 of 282 females (sample proportion 0.17), and 37 of 164 males (sample proportion 0.23). The pooled sample proportion was (48 + 37)/(282 + 164) = 0.19. Carry out a two-sided z test by hand to see if the difference in proportions who smoked between males and females was significant:
a. First calculate z, the standardized difference between sample proportions.
b. What can we say about the size of the P-value?
c. Was the difference significant?