Question

n 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 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 .

i need the null hypothesis,alternative hypothesis, value of the standard score for the sample proportion, critical value, P-value, what do you conclude ?

describe type I.type II error for this

Answer 1

(a)

H0: Null Hypothesis: p $\leq$ 0.5 ( Among smokers who try to quit with nicotine patch therapy, the majority are not smoking a year after the treatment )

(b)

HA: Alternative Hypothesis: p > 0.5 ( Among smokers who try to quit with nicotine patch therapy, the majority are smoking a year after the treatment ) (Claim)

(c)

n = Sample Size = 71

$\hat{p}$ = Sample Proportion = 39/71 = 0.5493

p = Population Proportion = 0.5

q = 1 - p = 0.5

SE = $\sqrt{pq/n}=\sqrt{0.5\times 0.5/71}=0.0593$

Value of the standard score for the sample proportion = Z = (0.5493 - 0.5)/0.0593 = 0.8308

(d)

$\alpha$ = 0.05

From Table, critical value of Z = 1.645

(e)

Table of Area Under Standard Normal Curve gives area = 0.2967

So,

p - value = 0.5 - 0.2967 = 0.2033

(f)

Since p - value = 0.2033 is greater than $\alpha$ = 0.05, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data support the claim that among smokers who try to quit with nicotine patch therapy, the majority are smoking a year after the treatment.

(g)

Type I Error: Rejection of a true null hypothesis.

Suppose in reality, among smokers who try to quit with nicotine patch therapy, the majority are not smoking a year after the treatment. We wrongly conclude that among smokers who try to quit with nicotine patch therapy, the majority are smoking a year after the treatment. Type I is committed in such a situation.

Type II Error: Failure to reject of a true null hypothesis.

Suppose in reality, among smokers who try to quit with nicotine patch therapy, the majority are smoking a year after the treatment. We wrongly conclude that among smokers who try to quit with nicotine patch therapy, the majority are not smoking a year after the treatment. Type II is committed in such a situation.