AP Statistics Section 10.3: Estimating a Population Proportion.
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Transcript of AP Statistics Section 10.3: Estimating a Population Proportion.
![Page 1: AP Statistics Section 10.3: Estimating a Population Proportion.](https://reader036.fdocuments.in/reader036/viewer/2022082518/5697c02a1a28abf838cd7efa/html5/thumbnails/1.jpg)
AP Statistics
• Section 10.3: Estimating a Population Proportion
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• Objective: To be able to create a confidence interval for a population proportion .
• Recall: • Parameter: p = population proportion• Statistic: = sample proportion• Inference is based on the sampling distribution of .• If certain conditions are met, . However in practice we
do NOT know .• Since is an unbiased estimator of we will estimate with
in our calculations.• Our new standard error for is
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• A level C confidence interval for . (1-proportion z-interval).• Conditions:• 1. Data is an SRS.• 2. Normality: n is so larger that and .• 3. Independence: a. Observations are independent.
OR b. When sampling without replacement, population 10n.
General form:
Notice that we are using z critical values instead of t critical values.
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Example: Spinning pennies. (pool data together)Create a 95% confidence interval for the true proportion of time a spinning penny falls heads up.
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Margin of Error and Choosing a Sample Size:To choose a sample size with a given margin of error, solve the following inequality for n:
where is eithera. ______ which is a conservative value for that will
maximize m. (Use this value as your default)b. could be a value based on prior experiments/studies
or results and may be a value other than the one in a.
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Example: What is the minimum sample size required to determine the percentage of time the spinning penny falls heads up with a margin of error of 1%?a. Conservative method
b. Use the historic value given in class to answer again.
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Example: A random sample of 71 MHS students revealed that 24 wanted to attend a state funded college or university. Create a 90% confidence interval for the true proportion of MHS students that want to attend a state funded college or university.
If we wanted the interval to have a width of no more than 8%, how many students would we need to sample? Use the conservative method.