Chap. 21 - Lecture Notes - SC

# Chap. 21 - Lecture Notes - SC - Chapter21 What is a...

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Chapter 21 What is a Confidence Interval?

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Review Questions When we discussed margin of error (MOE) in the beginning of the  semester, what was the quick method of finding it? A.  B. C. D. n 1 n n n p p n How do we find the sample proportion? A.  B. C. D. n success p # ˆ = n percent p = ˆ n success p # ˆ = success n p # ˆ =
What was the form of the confidence interval when we  discussed it in the beginning of the semester? A. Statistic  ±  MOE B. MOE  ±  Statistic C. Standard Deviation  ±  MOE D. Sample Size  ±  MOE Review Questions What was the level of confidence of the quick method  confidence interval we did earlier in the semester? A.  90%B.  95%C.  99%D.  99.7%

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Statistical Inference Statistics is divided into two branches, and statistics. is the process of collecting, organizing, describing data is the process of drawing conclusion about a population on the basis of data about a sample
Recall Numbers that describe a population are called while numbers that describe a sample are called Parameter Statistic Mean Proportion

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What Is A Confidence Interval? We are interested in estimating the true population  proportion, p. We already have one estimator for p,     . We have learned that the sampling distribution of the  sample proportion,       , is a approximately a normal  distribution. We also know that a normal distribution is completely  specified by the mean, μ, and the standard deviation,  . σ
What is a confidence interval? A confidence interval is an interval calculated from sample data by a process that is guaranteed to capture the true population parameter in of all samples. It is an estimate for the parameter +/- some margin of error In other words, once you have calculated a confidence interval, you can be 95% confident that the true proportion of the population is contained in that interval!

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What does 95% Confidence Mean? The 95% confidence interval for p will contain the true value of p in 95% of repeated samplings.
Recall that we found the sample  proportion The sample proportion,

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Recall: Sampling Distribution of a  Statistic The sampling distribution of a statistic is the distribution of values taken by the statistic in all possible samples of the same size from the same population .
Sampling Distribution of  p ˆ True value of p The sampling distribution of is approximately normal. The mean is equal to p.

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## This note was uploaded on 06/14/2011 for the course STAT 110 taught by Professor Johnson during the Spring '07 term at South Carolina.

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Chap. 21 - Lecture Notes - SC - Chapter21 What is a...

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