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Chapter 7 Outline

Objectives

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.

Introduction

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

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

term.

Formula

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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