Unit 7 Section 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 interest n = 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

 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

 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. Section 6.3

 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. Section 6.3

 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 Section 6.3

Formula for Minimum Sample Size Needed for Interval Estimate of a Population Proportion Section 6.3

 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 : #’s 1 – 23 ODD Section 6.3