In a study of smokers who tried to quit smoking with nicotine patch therapy, 39

Question

In a study of smokers who tried to quit smoking with nicotine patch therapy, 39 were smoking one year after the treatment, and 32 were not smoking one year after the treatment (based on data from “High-Dose Nicotine Patch Therapy,” by Dale et al., Journal of the American Medical Association, Vol. 274, No. 17). We want to 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 the treatment.

a. What is the null hypothesis?

b. What is the alternative hypothesis?

c. What is the value of the standard score for the sample proportion?

d. What is the critical value?

e. What is the P-value?

f. What do you conclude? (Be sure to address the original claim that among smokers who try to quit with nicotine patch therapy majority are smoking a year after the treatment).

g. Describe a type I error for this test.

h. Describe a type II error for this test.

i. What is the P-value if the claim is modified to state that the proportion is equal to 0.5?

Explanation / Answer

here let p is proportion of people who smoke after treatment

a) null hypothesis: p<=0.5

b) alternative hypothesis: p>0.5

c)value of standard score for the sample proportion phat=39/(32+39)=0.549

d)

critical value =1.645

e)as p=0.5 and n=32+39=71

std error =(p(1-p)/n)1/2 =0.059

therefore test stat z=(phat-p)/std error =0.8348

therefore p value =0.2019

f)as p value is greater then 0.05 level we can not reject null hypothesis.

there is not sufficient evidence to conclude that among smokers who try to quit with nicotine patch therapy, the majority are smoking a year after the treatment.

g) type I error : accepting that majority are smoking a year after the treatment when it is not true.

h) type II error : fail to reject that minority smoking a year after the treatment when it is not true.

i)

as then it will become 2 tailed test therefore

p value =2*0.2019 =0.4038

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