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# Chapter_07 - Statistics Chapter 7 Inferences Based on a...

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Chapter 7: Inferences Based on a Single Sample: Estimation with Confidence Interval Statistics

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McClave, Statistics, 11th ed. Chapter 7: Inferences Based on a Single Sample: Estimation by Confidence Intervals 2 Where We’ve Been Populations are characterized by numerical measures called parameters Decisions about population parameters are based on sample statistics Inferences involve uncertainty reflected in the sampling distribution of the statistic
McClave, Statistics, 11th ed. Chapter 7: Inferences Based on a Single Sample: Estimation by Confidence Intervals 3 Where We’re Going Estimate a parameter based on a large sample Use the sampling distribution of the statistic to form a confidence interval for the parameter Select the proper sample size when estimating a parameter

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7.1: Identifying the Target Parameter The unknown population parameter that we are interested in estimating is called the target parameter . McClave, Statistics, 11th ed. Chapter 7: Inferences Based on a Single Sample: Estimation by Confidence Intervals 4 Parameter Key Word or Phrase Type of Data µ Mean, average Quantitative p Proportion, percentage, fraction, rate Qualitative
7.2: Large-Sample Confidence Interval for a Population Mean A point estimator of a population parameter is a rule or formula that tells us how to use the sample data to calculate a single number that can be used to estimate the population parameter. McClave, Statistics, 11th ed. Chapter 7: Inferences Based on a Single Sample: Estimation by Confidence Intervals 5

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7.2: Large-Sample Confidence Interval for a Population Mean McClave, Statistics, 11th ed. Chapter 7: Inferences Based on a Single Sample: Estimation by Confidence Intervals 6 Suppose a sample of 225 college students watch an average of 28 hours of television per week, with a standard deviation of 10 hours. What can we conclude about all college students’ television time?
7.2: Large-Sample Confidence Interval for a Population Mean McClave, Statistics, 11th ed. Chapter 7: Inferences Based on a Single Sample: Estimation by Confidence Intervals 7 Assuming a normal distribution for television hours, we can be 95%* sure that 31 . 1 28 ) 67 (. 96 . 1 28 225 10 96 . 1 28 96 . 1 ± = ± = ± = ± = μ σ n x *In the standard normal distribution, exactly 95% of the area under the curve is in the interval -1.96 … +1.96

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Interval for a Population Mean McClave, Statistics, 11th ed. Chapter 7: Inferences Based on a Single Sample: Estimation by Confidence Intervals 8 An interval estimator or confidence interval is a formula that tell us how to use sample data to calculate an interval that estimates a population parameter. x
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Chapter_07 - Statistics Chapter 7 Inferences Based on a...

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