Answered: Incentives for Quitting Smoking: Do…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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Incentives for Quitting Smoking: Do They Work?

Exercise 5.31 describes a study examining incentives to quit smoking. With no incentives, the proportion of smokers trying to quit who are still abstaining six months later is about 0.06. Participants in the study were randomly assigned to one of four different incentives, and the proportion successful was measured six months later. Of the 498 participants in the group with the least success, 47 were still abstaining from smoking six months later. We wish to test to see if this provides evidence that even the smallest incentive works better than the proportion of 0.06 with no incentive at all.

(a)

State the null and alternative hypotheses, and give the notation and value of the sample statistic.

(b)

Use a randomization distribution and the observed sample statistic to find the p-value.

(c)

Give the mean and standard error of the normal distribution that most closely matches the randomization distribution, and then use this normal distribution with the observed sample statistic to find the p-value.

(d)

Use the standard error found from the randomization distribution in part (b) to find the standardized test statistic, and then use that test statistic to find the p-value using a standard normal distribution.

(e)

Compare the p-values from parts (b), (c), and (d). Use any of these p-values to give the conclusion of the test.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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