EBK PRACTICE OF STATISTICS IN THE LIFE
EBK PRACTICE OF STATISTICS IN THE LIFE
4th Edition
ISBN: 9781319067496
Author: BALDI
Publisher: VST
Question
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Chapter 20, Problem 20.1AYK
To determine

To give a 95% confidence interval for the difference between the proportions of smokers who still abstain from smoking six months after they stopped when quitting either abruptly or gradually.

Expert Solution & Answer
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Answer to Problem 20.1AYK

  (0.0071,0.1224) .

Explanation of Solution

In the question, it is given that verified abstinence was achieved at that point by 78 of 355 subjects in the abrupt-cessation group and 53 of the 342 subjects in the gradual-cessation group. Thus, we know that the subjects were chosen randomly for the study and also the conditions for large-sample is satisfied because we have,

  x1×p1>10x2×p2>10

Thus, the proportions are as follows:

  p^1=x1n1=78355=0.2197p^2=x2n2=53342=0.1550

Thus, the 95% confidence interval for the difference between the proportions of smokers can be calculated as:

  SE=p^1(1p^1)n1+2+p^2(1p^2)n2+2=0.2197(10.2197)355+0.1550(10.1550)342=0.0294zα/2=z0.025=1.96Confidence interval=(0.21970.1550)±1.96×0.0294=0.0647±0.0577=(0.0071,0.1224)

So, we are 95% confident that the difference between the proportions of smokers who still abstain from smoking six months after they stopped when quitting either abruptly or gradually is between (0.0071,0.1224) .

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