# Fifteen percent of Australians smoke. By introducing tough laws banning brand labels on cigarette packages, Australia hopes to reduce the percentage of people smoking to 10% by 2018 (Reuters website, October 23, 2012). Answer the following questions based on a sample of 240 Australians. a. Show the sampling distribution of p ¯ , the proportion of Australians who are smokers. b. What is the probability the sample proportion will be within ±.04 of the population proportion? c. What is the probability the sample proportion will be within ±.02 of the population proportion?

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

13th Edition
Anderson
Publisher: CENGAGE L
ISBN: 9781305881884

#### Solutions

Chapter
Section
Chapter 7, Problem 50SE
Textbook Problem
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## Fifteen percent of Australians smoke. By introducing tough laws banning brand labels on cigarette packages, Australia hopes to reduce the percentage of people smoking to 10% by 2018 (Reuters website, October 23, 2012). Answer the following questions based on a sample of 240 Australians. a. Show the sampling distribution of p ¯ , the proportion of Australians who are smokers. b. What is the probability the sample proportion will be within ±.04 of the population proportion? c. What is the probability the sample proportion will be within ±.02 of the population proportion?

Expert Solution

a.

To determine

Show the sampling distribution of p¯, the proportion of Australians who are smokers.

### Explanation of Solution

Calculation:

The given information is that sample of 240 Australians is questioned. The percentage of people smoking is 15%.

Sampling distribution of p¯:

The probability distribution all possible values of the sample proportion p¯ is termed as the sampling distribution of p¯.

• The expected value of p¯ is, E(p¯)=p.
• The standard deviation of p¯ is

For finite population, σp¯=NnN1p(1p)n

For infinite population, σp¯=p(1p)n

• When np5 and n(1p)5 then the sampling distribution of p¯ is approximated by a normal distribution.

The expected value is,

E(p¯)=p=0

Expert Solution

b.

To determine

Find the probability that the sample proportion will be within ±.04 of the population proportion.

Expert Solution

c.

To determine

Find the probability that the sample proportion will be within ±.02 of the population proportion.

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