Question : A study on the effectiveness of nicotine patch was carried out. Of 120 volunteers randomly assigned to use a nicotine patch, 55 had quit smoking after 8 weeks.

i) What is the proportion of them who did not benefit from the nicotine patch ?

ii) Determine the 97% confidence interval for the proportion of those who benefited from the nicotine patch.

iii) How large a sample should be taken if the desired margin error at 97% for the population proportion of quitting smoking to be within 0.2?