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
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,