ap statistics section 10.3: estimating a population proportion
TRANSCRIPT
AP Statistics
• Section 10.3: Estimating a Population Proportion
• 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
• 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.
Example: Spinning pennies. (pool data together)Create a 95% confidence interval for the true proportion of time a spinning penny falls heads up.
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.
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.
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.