ABSTRACT
Point estimates In estimating, we could use a single value to estimate the true population mean. For example, if the grade point average of a random sample of students is 3.75 then we might estimate that the population average of all students is also 3.75. Or, we might select at random 20 items of inventory from a distribution centre and calculate that their average value is £25.45. In this case we would estimate that the population average of the entire inventory is £25.45. Here we have used the sample mean x-as a point estimate or an unbiased estimate of the true population mean, μx. The problem with one value or a point estimate is that they are presented as being exact and that unless we have a super
After you have studied this chapter you will understand how sampling can be extended to make estimates of population parameters such as the mean and the proportion. To facilitate comprehension the chapter is organized as follows:
✔ Estimating the mean value • Point estimates • Interval estimates • Confidence level and reliability • Confidence interval of the mean for an infinite population • Application of confidence intervals for an infinite population: Paper • Sample size for estimating the mean of an infinite population • Application for determining the sample size: Coffee • Confidence interval of the mean for a finite population • Application of the confidence interval for a finite population: Printing
✔ Estimating the mean using the Student-t distribution • The Student-t distribution • Degrees of freedom in the t-distribution • Profile of the Student-t distribution • Confidence intervals using a Student-t distribution • Excel and the Student-t distribution • Application of the Student-t distribution: Kiwi fruit • Sample size and the Student-t distribution • Re-look at the example kiwi fruit using the normal distribution
✔ Estimating and auditing • Estimating the population amount • Application of auditing for an infinite population: tee-shirts • Application of auditing for a finite population: paperback books
✔ Estimating the proportion • Interval estimate of the proportion for large samples • Sample size for the proportion for large samples • Application of estimation for proportions: Circuit boards
✔ Margin of error and levels of confidence • Explaining margin of error • Confidence levels
cisely the right value is low. Point estimates are often inadequate as they are just a single value and thus, they are either right or wrong. In practice it is more meaningful to have an interval estimate and to quantify these intervals by probability levels that give an estimate of the error in the measurement.
