. In a study of smokers who tried to quit smoking with nicotine patch therapy, 3

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 sig- nificance level to test the claim that among smokers who try to quit with nicotine patch therapy, the majority are smok- ing 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 nico- tine patch therapy, the majority are smoking a year the treatment.) Describe a type I error for this test. ribe a type II error for this test. P-value if the claim is modified to state that the proportign sequal to 0.5

Explanation / Answer

Part a

Null hypothesis: H0: The proportion of persons who quit smoking is 50% or less.

H0: p 0.5

Part b

Alternative hypothesis: Ha: The proportion of persons who quit smoking is more than 50%.

Ha: p > 0.5

Part c

We are given X = 39

N = 39+32 = 71

Sample proportion = P = X/N = 93/71 = 0.549295775

Part d

Critical value = 1.6449

(by using z-table)

Part e

Test statistic = Z = (P – p) / sqrt(p(1 – p)/N)

Z = (0.549295775 – 0.5) / sqrt(0.5*(1 – 0.5)/71)

Z = 0.8307

P-value = 0.2031

(By using z-table)

Part f

Here, p-value > level of significance = alpha = 0.05, so we do not reject the null hypothesis that proportion of persons who quit smoking is 50% or less.

There is insufficient evidence to conclude that among smokers who try to quit with nicotine patch therapy, the majority are smoking a year the treatment.

Part g

Type I error = Probability of rejecting the null hypothesis that proportion of persons who quit smoking is 50% or less when actually it is true.

Part h

Type II error = Probability of do not rejecting the null hypothesis that proportion of persons who quit smoking is 50% or less when actually it is not true.

Part i

Required p-value = 2*0.2031 = 0.4061

(By using part e)

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