Unit 7Section 6.3

6.3: Confidence Intervals for Population Proportions Proportion – a part of a whole. Can be

represented as a percent, decimal, or fraction.

Notation: p = population proportion = sample proportion (read as “p hat”)

For a sample proportion,

and

where X = the number of sample units that

possess the characteristics of interestn = sample size

Section 6.3

Example 1:In a recent survey of 150

households, 54 had central air conditioning. Find and , where is the proportion that have central air conditioning.

Section 6.3

Section 6.3

Similar to means, one can estimate a population proportion using a sample proportion.

Sample proportions can be used as our point estimate.

A confidence interval is once again used to estimate the population proportion.

Formula for a Specific Confidence Interval for a proportion

where and

Rounding Rule: Round to three decimal places

Section 6.3

EppEp ˆˆ

5np 5nq

n

qpzE c

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Example 2:A sample of 500 nursing

applications included 60 from men. Find the 90% confidence interval of the true proportion of men who applied for the nursing program.

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Example 3:A sample of 200,000 boat owners

found that 12% of the pleasure boats were named Serenity. Find the 95% confidence interval of the true proportion of boats names Serenity.

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Proportions can also be used to determine the sample size needed for a specific confidence interval

If the initial proportion is unknown, we

assign 0.5 to the value of

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Formula for Minimum Sample Size Needed for Interval Estimate of a

Population Proportion

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Example 4:A researcher wishes to estimate,

with 95% confidence, the proportion of people who own a home computer. A previous study shows that 40% of those interviewed had a computer at home. The researcher wishes to be accurate within 2% of the true proportion. Find the minimum sample size needed

Section 6.3

Example 5:The same researcher wishes to

estimate the proportion of executives who own a car phone. She wants to be 90% confident and be accurate within 5% of the true proportion. Find the minimum sample size needed.

Section 6.3

Homework: Pgs. 325 - 327: #’s 1 – 23 ODD

Section 6.3