 # A random sample of 100 patients treated in a program for alcoholism and drug dependency over the past 10 years was selected. It was determined that 53 of the patients had been readmitted to the program at least once. At the 95% level, construct an estimate of the population proportion. ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836 ### Essentials Of Statistics

4th Edition
HEALEY + 1 other
Publisher: Cengage Learning,
ISBN: 9781305093836

#### Solutions

Chapter
Section
Chapter 6, Problem 6.12P
Textbook Problem
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## A random sample of 100 patients treated in a program for alcoholism and drug dependency over the past 10 years was selected. It was determined that 53 of the patients had been readmitted to the program at least once. At the 95% level, construct an estimate of the population proportion.

Expert Solution
To determine

The estimate the proportion of the population using the 95% confidence level.

### Explanation of Solution

Given Information:

A random sample of 100 patients treated in a program for alcoholism and drug dependency over the past 10 years was selected. It was determined that 53 of the patients had been readmitted to the program at least once.

X¯=53N=100

Formula used:

Confidence interval for a sample proportion (large sample) is given by,

c.i.=Ps±ZPu(1Pu)N

Calculation:

From the given information,

Ps=X¯N=53100=0.53

The value of statistic at 95% level of significance is given as,

Z0.05=1.96

Substitute 0

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