Question

In one study of smokers who tried to quit smoking with nicotine patch​ therapy, 38 were smoking one year after treatment and 30 were not smoking one year after the treatment. Use a 0.10 significance level to test the claim that among smokers who try to quit with nicotine patch​ therapy, the majority are smoking one year after the treatment. Do these results suggest that the nicotine patch therapy is not​ effective? N= 68

find t-statistic and p-value

Answer 1

Answers to questions asked:

t statistic = 0.9703

p - value = 0.1660

EXPLANATION:

H0: Null Hypothesis: P 0.5

HA: Alternative Hypothesis: P > 0.5

n = Sample Size = 68

= Sample Proportion = 38/68 = 0.5588

P = Population Proportion

Q = 1 - P = 0.5

SE =

Test statistic is:
Z = (0.5588 - 0.5)/0.0606 = 0.9703

Table of Area Under Standard Normal Curve gives area = 0.3340

So,

p - value=0.5 - 0.3340 = 0.1660

Since p - value= 0.1660 is greater than = 0.10, the difference is not significant. Fail to reject null hypothesis.

= 0.10

One Tail - Right Side Test

From Table, critical value of Z = 1.2816

Since the calculated value of Z = 0.9703 is critical value of Z = 1.2816, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that among smokers who try to quit with nicotine patch therapy, the majority are smoking one year after the treatment.