ESTIMATION OF THE MEAN

2 INTRO :: ESTIMATION Definition The assignment of plausible value(s) to a population parameter based on a value of a sample statistic is called estimation.

3 INTRO :: ESTIMATION The sample statistic used to estimate a population parameter is called estimator. Examples … sample mean estimator population mean …

4 INTRO :: ESTIMATION 1. Select a sample. 2. Collect the required information from the members of the sample. 3. Calculate the value of the sample statistic. 4. Assign plausible value(s) to the corresponding population parameter. The estimation procedure involves …

5 POINT ESTIMATES & INTERVAL ESTIMATES A Point Estimate An Interval Estimate

6 A Point Estimate Definition The value of a sample statistic that is used to estimate a population parameter is called a point estimate.

7 INTERVAL ESTIMATES Usually, whenever we use point estimation, we calculate the margin of error associated with that point estimation. Point Estimate w/out M.E. not very useful!!!!

8 Interval Estimates Definition In interval estimation, an interval is constructed around the point estimate, and it is stated that this interval is likely to contain the corresponding population parameter. Gives a range of plausible values for the parameter of interest.

9 Interval estimation. $1130$1610

10 Interval Estimates Definition Each interval is constructed with regard to a given confidence level and is called a confidence interval. The confidence level associated with a confidence interval states how much confidence we have that this interval contains the true population parameter. The confidence level is denoted by (1 – α)100%.

11 INTERVAL ESTIMATION OF A POPULATION MEAN: Confidence Interval for μ w/ Large Sample The (1 – α )100% confidence interval for μ is The value of z used here is read from the standard normal distribution table for the given confidence level.

12 Finding z for a 95% confidence level. μ z x Total shaded area is.9500 or 95%