# Constructing a confidence interval for a proportion

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Constructing a Confidence Interval for a ProportionRecall: The possible sample proportions are bell-shaped with a mean of and standard deviation of Issue: Don’t know the true population proportion Substitute the sample proportion for the true proportion in the formula to obtain the standard error of the sample proportions (SEP)?^?=?(1?)????=^?(1^?)?STAT 206
C.I. estimate for the ProportionWhen nis large, a confidence interval for a population proportion p, based on a sample of size nfrom that population, with sample proportion is:
ExampleOut of 575 randomly selectedpatients of a local hospital who were surveyed, 312 reported that they were satisfied with the care they received.Construct andinterpret a 95% confidence interval for the percentage of all patients satisfied with their care at the hospital.?
ExampleOut of 575 randomly selectedpatients of a local hospital who were surveyed, 312 reported that they were satisfied with the care they received.Construct andinterpret a 95% confidence interval for the proportion of patients satisfied with their care at the hospital.?
STAT 206
EXAMPLE: The operations manager at a large newspaper wants to estimate the proportion of newspapers printed that have a nonconforming attribute. Nonconforming attributes consist of excessive rub-off, improper page setup, missing pages, or duplicate pages. The manager selects a random sample of 200 newspapers, which 35 newspaper contain some type of nonconformance. Construct and interpret a 90% confidence interval for the proportion of newspapers printed during the day that have a nonconforming attribute. ?
EXAMPLE: The operations manager at a large newspaper wants to estimate the proportion of newspapers printed that have a nonconforming attribute. Nonconforming attributes consist of excessive rub-off, improper page setup, missing pages, or duplicate pages. The manager selects a random sample of 200 newspapers, which 35 newspaper contain some type of nonconformance. Construct and interpret a 90% confidence interval for the proportion of newspapers printed during the day that have a nonconforming attribute. ?
STAT 206
Examining C.I. for the ProportionMarginof Error2.