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Outline Of Chapter 7 Text Elementary Statistics: A Brief Version(A. Bluman 3rd Ed., 2003)

815 words - 3 pages

Chapter 7 Outline

Find the confidence interval for the mean when s is known or n > 30.
Determine the minimum sample size for finding a confidence interval for the mean.
Find the confidence interval for the mean when s is unknown and n < 30.
Objectives (cont'd.)
Find the confidence interval for a proportion.
Determine the minimum sample size for finding a confidence interval for a proportion.
Find a confidence interval for a variance and a standard deviation.
Estimation is the process of estimating the value of a parameter from information obtained from a sample.
Three Properties of a Good Estimator
The estimator should be an unbiased estimator. That is, the expected value or the mean of the estimates obtained from samples of a given size is equal to the parameter being estimated.
The estimator should be consistent. For a consistent estimator, as sample size increases, the value of the estimator approaches the value of the parameter estimated.
The estimator should be a relatively efficient estimator; that is, of all the statistics that can be used to estimate a parameter, the relatively efficient estimator has the smallest variance.
Point and Interval Estimates
A point estimate is a specific numerical value of a parameter. The best point estimate of the population mean m is the sample mean .

Confidence Level and Confidence Interval

The confidence level of an interval estimate of a parameter is the probability that the interval estimate will contain the parameter.

A confidence interval is a specific interval estimate of a parameter determined by using data obtained from a sample and by using the specific confidence level of the estimate.

Formula for the Confidence Interval of the Mean for a Specific a

For a 95% confidence interval, ;
and for a 99% confidence interval,
Maximum Error of Estimate
The maximum error of estimate is the maximum likely difference between the point estimate of a parameter and the actual value of the parameter. It is represented by the
Formula for the Minimum Sample Size Needed for an Interval Estimate of the Population Mean

where E is the maximum error of estimate. If there is any fraction or decimal portion in the answer, use the next whole number for sample size, n.
t Distribution
Finding Confidence Intervals for the Mean (s unknown and n < 30)
When the population sample size is less than 30, and the standard deviation is unknown, the t distribution must be used.
Characteristics of the t Distribution
The t distribution is similar to the standard normal distribution in...

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