Question

In one study of smokers who tried to quit smoking with nicotine patch​ therapy, 35 were smoking one year after treatment and 34 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?

The test statistic for this hypothesis test is _

Identify the P Value for this hypothesis test

Answer 1

SOLUTION:

From given data,

In one study of smokers who tried to quit smoking with nicotine patch​ therapy, 35 were smoking one year after treatment and 34 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.

EXPLANATION:

H₀: Null Hypothesis: P < 0.5

H_A: Alternative Hypothesis: P > 0.5

n = Sample Size =35+34 = 69

= Sample Proportion = 35/69 =0.5072

P = Population Proportion

Q = 1 - P = 1-0.5=0.5

= 0.06019

Test statistic is:

Z = (0.5072 - 0.5)/ 0.06019

= 0.11962

approx 0.12

Table of Area Under Standard Normal Curve gives area = 0.04776

So,

p - value = 0.5 - 0.04776 = 0.45224

Since p - value= 0.45224 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 = 0.11962 is critical value of Z = 1.2816, the difference is not significant. Fail to reject null hypothesis.