Question

Nicotine patches are often used to help smokers quit. Does adding antidepressants to the nicotine patches help? A randomized double-blind experiment assigned 250 to receive a patch that includes the antidepression drug bupropion and 232 smokers who wanted to stop to receive regular nicotine patches. After a year, 95 in the patch & drug group had abstained from smoking and 49 subjects in the nicotine patch group.

p̂patch & drug	=  ________
p̂patch	= ________

Find a 90% confidence interval for the difference (treatment minus control) in the proportion of smokers who quit.

____________

Conclusion

a. - The patch/bupropion combination decreases the success rate by this interval over the patch alone 90% of the time.

b. - We are 90% confident that the patch/bupropion combination decreases the success rate by this interval over the patch alone.    

c. - The patch/bupropion combination increases the success rate by this interval over the patch alone 90% of the time.

d. -We are 90% confident that the patch/bupropion combination increases the success rate by this interval over the patch alone.

Answer 1

Here, , n1 = 250 , n2 = 232

p̂patch & drug   = 0.38
p̂patch   = 0.2112

Standard Error, sigma(p1cap - p2cap),
SE = sqrt(p1cap * (1-p1cap)/n1 + p2cap * (1-p2cap)/n2)
SE = sqrt(0.38 * (1-0.38)/250 + 0.2112*(1-0.2112)/232)
SE = 0.0407

For 0.9 CI, z-value = 1.64
Confidence Interval,
CI = (p1cap - p2cap - z*SE, p1cap - p2cap + z*SE)
CI = (0.38 - 0.2112 - 1.64*0.0407, 0.38 - 0.2112 + 1.64*0.0407)
CI = (0.1021 , 0.2355)

d. -We are 90% confident that the patch/bupropion combination increases the success rate by this interval over the patch alone.