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Chapter 11: Q. 39 (page 755)

How to quit smoking Refer to Exercise 37. Which treatment seems to be most effective? Least effective? Justify your choices.

Short Answer

Expert verified

The most effective treatment is a patch plus drug and the least effective is a Nicotine patch.

Step by step solution

01

Given information

We need to find the most effective and least effective treatment to quit smoking.

02

Explanation

We know that

Expected frequencies are a product of row and column total divided by table total. So,

ROW AND COLUMN NUMBEREXPECTED FREQUENCY
E11
61.75
E12
182.25
E21
61.75
E22
182.25
E31
62.00
E32
183.00
E41
40.49
E42
119.51

For the treatment Nicotine patch, the predicted frequency of the number of successes deviates the greatest from the observed frequency, despite the fact that the expected frequency is higher than the observed frequency (expected 61.75and observed 40). As a result, the Nicotine Patch is the least effective treatment option.

We note that for the therapy Patch plus medicine, the predicted frequency of the number of successes deviates the most from the observed frequency, while the expected frequency is lower than the observed frequency (expected 62.00and observed 87). As a result, the most successful treatment is the Patch with medication.

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Most popular questions from this chapter

Popular kids Who were the popular kids at your elementary school? Did they get good grades or have good looks? Were they good at sports? A study was performed in Michigan to examine the factors that determine social status for children in grades 4,5,and 6. Researchers administered a questionnaire to a random sample of 478students in these grades. One of the questions asked, "What would you most like to do at school: make good grades, be good at sports, or be popular?" The two-way table summarizes the students' responses. Is there convincing evidence of an association between gender and goal for students in grades 4,5,and 6?

Is your random number generator working? Use your calculator’s RandInt function to generate 200 digits from 0 to 9 and store them in a list.

a. State appropriate hypotheses for a chi-square test for goodness of fit to determine whether your calculator’s random number generator gives each digit an equal chance of being generated.

b. Carry out a test at the α=0.05 significance level. Hint: To obtain the observed

counts, make a histogram of the list containing the 200 random digits, and use the trace feature to see how many of each digit were generated. You may have to adjust your window to go from −0.5to9.5 with an increment of 1

c. Assuming that a student’s calculator is working properly, what is the probability that the student will make a Type I error in part (b)?

d. Suppose that 25 students in an AP® Statistics class independently do this exercise for homework and that all of their calculators are working properly. Find the probability that at least one of them makes a Type I error.

Which of the following is the correct number of degrees of freedom for the chi-square test using these data?

a.4

b.8

c. 10

d.20

e.4876

A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race or ethnicity of the driver. The results are summarized in the following table.

The proportion of this city's population in each of the racial/ethnic categories listed is as follows.

We wish to test H0: The racial/ethnic distribution of traffic tickets in the city is the same as the racial/ethnic distribution of the city's population.

The category that contributes the largest component to the χ2test statistic is a. White, with 12.4fewer tickets than expected.

b. White, with 12.4more tickets than expected.

c. Hispanic, with 6.16fewer tickets than expected.

d. Hispanic, with 6.16more tickets than expected.

Opinions about the death penaltyThe General Social Survey (GSS) asked separate random samples of people with only a high school degree and people with a bachelor’s degree, “Do you favor or oppose the death penalty for persons convicted of murder?” Of the 1379people with only a high school degree, 1010 favored the death penalty, while 319of the 504people with a bachelor’s degree favored the death penalty. We can test the hypothesis of “no difference” in support for the death penalty among people in these educational categories in two ways: with a two-sample z test or with a chi-square test.

a. State appropriate hypotheses for a chi-square test.

b. Here is Minitab output for a chi-square test. Interpret the P-value. What conclusion would you draw?

c. Here is Minitab output for a two-sample z test. Explain how these results are consistent with the test in part (a).
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