Chapter Seven

Chapter Seven - Lecture Notes Chapter Seven Inferences...

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Lecture Notes Chapter Seven: Inferences Based on a Single Sample: Estimation with Confidence Intervals Randall Miller 1 | Page 1. Identifying the Target Parameter Definition 7.1 The unknown population parameter (e.g., mean or proportion) that we are interested in estimating is called the target parameter . Determining the Target Parameter Parameter Key Words or Phrases Type of Data µ Mean; average Quantitative p Proportion; percentage; fraction; rate Qualitative 2. Large-Sample Confidence Interval for a Population Mean Definition 7.2 An interval estimator (or confidence interval ) is a formula that tells us how to use sample data to calculate an interval that estimates a population parameter. Definition 7.3 The confidence interval is the probability that an interval estimator encloses the population parameter – that is, the relative frequency with which the interval estimator encloses the population parameter when the estimator is used repeatedly a very large number of times. The confidence level is the confidence coefficient expressed as a percentage. Definition 7.4 The value z α is defined as the value of the standard normal random variable z such that the area will lie to its right. In other words, ( ) Pz z >= . Commonly Used Values of /2 z Confidence Level ( ) 100 1 z 90% 0.10 0.05 1.645 95% 0.05 0.025 1.96 99% 0.01 0.005 2.575

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Lecture Notes Chapter Seven: Inferences Based on a Single Sample: Estimation with Confidence Intervals Randall Miller 2 | Page Large-Sample ( ) α 100 1- % Confidence Interval for µ The large-sample ( ) 100 1 % α confidence interval for is /2 x xz n αα σ ±= ±
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Chapter Seven - Lecture Notes Chapter Seven Inferences...

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