Question

Complete the following chapter review exercise out of your textbook:

• Exercise 2 (a–i), p. 338

In this exercise, you will practice the steps of working through a hypothesis–testing problem.

You will submit a Microsoft Word document with your answers to the questions.

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

1. What is the null hypothesis
2. What is the alternative hypothesis
3. What is the value of the standard score for the sample proportion?
4. What is the critical value?
5. What is the P-value?
6. What do you conclude? (Be sure to address the original claim that among smokers who try to quit with nicotine patch therapy, the majority are smoking a year the treatment.)
7. Describe a type I error for this test
8. Describe a type II error for this test
1. What is the P-value if the claim is modified to state that the proportion is equal to 0.5?

Answer 1

A. What is the null hypothesis

Let p be the proportion of who were smoking a year after the treatment.

Null hypothesis H0: Among smokers who try to quit with nicotine patch therapy, the proportion of smokers and non-smokers a year after the treatment are equal. That is p = 0.5

B. What is the alternative hypothesis

Alternative hypothesis H0: Among smokers who try to quit with nicotine patch therapy, the majority are smoking a year after the treatment. That is p > 0.5

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

Sample size = 39 + 32 = 71

Sample proportion, p = 39 / 71 = 0.5493

Standard error of proportion = = 0.05905

The standard score, z = (0.5493 - 0.5) / 0.05905 = 0.835

D. What is the critical value?

The critical value of Z at 0.05 significance level and right tail test is 1.64

E. What is the P-value?

P-value = P(Z > 0.835) = 0.2019

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

Since p-value is greater than the significance level of 0.05, we fail to reject null hypothesis H0 and conclude that there is no significant evidence that among smokers who try to quit with nicotine patch therapy, the majority are smoking a year the treatment.

G. Describe a type I error for this test

Type I error is that we conclude that the majority are smoking a year the treatment but in reality the proportion of smokers and non-smokers a year after the treatment are equal.

H. Describe a type II error for this test

Type II error is that we fail to conclude that the majority are smoking a year the treatment but in reality the proportion of smokers a year after the treatment are greater than 0.5.

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

If the claim is modified to state that the proportion is equal to 0.5, this will become a two-tail test and

P-value = 2 * P(Z > 0.835) = 2 * 0.2019 = 0.4038