Chapter 9

Chapter 9 - Chapter 9: Point Estimates and Confidence...

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1 Chapter 9: Point Estimates and Confidence Intervals 1. Review of Sampling a. Sample is a subset of a population b. Reasons for sampling i. To contact the whole population would be very time consuming ii. The cost of studying all the items in the population is prohibitive iii. It is physically impossible to check all the items in the population iv. The nature of the test is destructive v. A sample adequately represents the rest of the population c. Methods of sampling i. Simple random sampling ii. Systematic random sampling iii. Stratified random sampling iv. Cluster sampling b. Sampling error is the difference between a sample statistic and its corresponding population parameter i. Example: X μ ! c. Sampling distribution i. Suppose all possible samples of size n are selected from a specified population, and the mean of each sample is computed. We could then find the distribution of all the means. ii. The mean of all the sample means is exactly equal to the population mean iii. If the population from which the samples are drawn is normal, the distribution of the sample means is also normally distributed iv. If the population from which the samples are drawn is not normal, the sampling distribution is approximately normal if the samples are sufficiently large (at least 30 observations or if binomial data then 5 n ! > and (1 ) 5 n " > ) 2. Statistical Inferences a. We use sampling to estimate characteristics of the population i. Parameter is a characteristic of the population ii. The population is large or it is difficult to identify all members of the population and so we are unable to take all possible samples from the population.
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2 b. Point estimate i. A point estimate is a single statistic used to estimate a population parameter ii. Example of point estimates 1. The sample mean, X , is a point estimate for the population mean, μ 2. The sample proportion, p, is a point estimate for the population proportion, ! 3. The sample standard deviation, s, is a point estimate for the population standard deviation, Parameter Statistic Mean x Standard deviation s Proportion p Correlation r iii. We expect the point estimate to be close to the population parameter but not exactly the same as the population parameter due to sampling error iv. Example: A manufacturer of batteries for portable hand tools wishes to investigate the length of time a battery will last. A sample of 12 batteries had a mean length of time of 4.3 hours. We know that the standard deviation of battery life is 0.3 hours for the population. 1. Why do we sample in this case? 2. What is the point estimate? 3. If all the batteries last an average of 4 hours, what is the sampling error? c.
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Chapter 9 - Chapter 9: Point Estimates and Confidence...

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