1. 8.3 Estimating Population Proportions
LEARNING GOAL
Learn to estimate population proportions and compute the associated margins of error and confidence intervals.
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2. The Basics of Estimating a Population Proportion
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3. 95% Confidence Interval for a Population Proportion
For a population proportion, the margin of error for the 95% confidence interval is
where is the sample proportion.
The 95% confidence interval ranges
from – margin of error to margin of error
We can write this confidence interval more formally as
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4. EXAMPLE 1 TV Nielsen Ratings
The Nielsen ratings for television use a random sample of households. A Nielsen survey results in an estimate that a women’s World Cup soccer game had 72.3% of the entire viewing audience. Assuming that the sample consists of n = 5,000 randomly selected households, find the margin of error and the 95% confidence interval for this estimate.
Solution:
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5. Choosing Sample Size Choosing the Correct Sample Size
In order to estimate a population proportion with a 95% degree of confidence and a specified margin of error of E, the size of the sample should be at least
n = 1
E 2
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6. EXAMPLE 2 Minimum Sample Size for Survey
You plan a survey to estimate the proportion of students on your campus who carry a cell phone regularly. How many students should be in the sample if you want (with 95% confidence) a margin of error of no more than 4 percentage points?
Solution:
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