Question: A study used nicotine gum to help people quit smoking

A study used nicotine gum to help people quit smoking. The study was placebo-controlled, randomized, and double-blind. Each participant was interviewed after 28 days, and success was defined as being abstinent from cigarettes for 28 days. The results showed that 174 out of 1649 people using the nicotine gum succeeded, and 66 out of 1648 using the placebo succeeded. Although the sample was not random, the assignment to groups was randomized. (Source: Shiffman et al., Quitting by gradual smoking reduction using nicotine gum: A randomized controlled trial, American Journal of Preventive Medicine, vol. 36, issue 2, February, 2009)
a. Find the proportion of people using nicotine gum that stopped smoking and the proportion of people using the placebo that stopped smoking, and compare them. Is this what the researchers had expected?
b. Find the observed value of the test statistic, assuming that the conditions for a two-proportion z-test hold.

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