General Concepts of Estimation

Point estimate

A point estimate is one value ( a point) that is used to estimate a population parameter.

Examples of point estimates are the sample mean, the sample standard deviation, the sample variance, the sample proportion etc...

EXAMPLE: The number of defective items produces by a machine was recorded for five randomly selected hours during a 40-hour work week, The observed number of defectives were 12, 4, 7, 14 and 10. So the sample mean is 9.4  thus a point estimate for hourly mean number of defectives is 9.4.

 Interval Estimate

• An Interval Estimate states the range within a population parameter probably lies. 
• The  interval within a population parameter is expected to occur is called a confidence interval.
• The  two confidence intervals that are used extensively are the 95% and the 99%
• The confidence level describes the uncertainty associated with a sampling  method.
• Suppose we used the same sampling method to select different samples and to compute a different interval estimate for each sample. some interval estimates would include the true population parameter and some would not. A 90% confidence level means that we would expect 90% of the interval estimates to include the population parameter.
• A 95% confidence interval means 95% of the sample means for a specified sample size will lie within 1,96 standard deviations of the hypothesized population mean.
• For the 99% confidence interval, 99% of the sample means for a specified sample size will lie within 2.58 standard deviation of the hypothesized population mean.