Question

In one study of smokers who tried to quit smoking with nicotine patch therapy, 50 were smoking one year after the treatment, and 34 were not smoking one year after the treatment. Use a 0.05 significance level to test the claim that among smokers who try to quit with nicotine patch therapy, the majority are smoking a year after treatment.

Answer 1

H0: p = 0.50

Ha: p > 0.50

Sample prroportion = 34/50 = 0.68

Test Statistic :-
Z = ( - P ) / ( √((P * ( 1 - P) )/n)
Z = ( 0.68 - 0.5 ) / ( √(( 0.5 * 0.5) /50))
Z = 2.55

Decision rule :-
Reject null hypothesis if Z > Z(α)
Z(α/2) = Z(0.05) = 1.645
Z > Z(α) = 2.5456 > 1.645, hence we reject the null hypothesis

We have sufficient evidence to support the claim that among smokers who try to quit with nicotine patch therapy,  the majority are smoking a year after treatment.