MATHM6_Estimation-of-Parameters_Part-1.pptx

MATHM6_Estimation-of-Parameters_Part-1.pptx

1. E stimation of Parameters UNIT II MODULE 6

2. PART 1 Point Estimation

3. Learning Targets Differentiate descriptive and inferential statistics Define, differentiate and illustrate point estimation and interval estimation Discuss the properties of a good estimator Use a point estimator to estimate the population mean and population variance

4. DESCRIPTIVE STATISTICS vs INFERENTIAL STATISTICS DESCRIPTIVE STATISTICS - aims to describe the characteristics of data - process of using or analyzing those measures that quantitatively describe or summarize features from a collection of information INFERENTIAL STATISTICS - aims to make inferences or predictions - pertains to the process of drawing and making decisions concerning a given population based on the data obtained from a sample - focuses on estimation and hypothesis testing

5. Estimation A process used to calculate the proposed values for parameters by using only a random sample from the population. Being done because population parameters are usually unknown and /or the population is infeasible to study Note: The results from estimation may not always be accepted since it is preferred that interpretations and generalizations must be made using data from the entire population. Thus, it is necessary to do hypothesis testing.

6. POINT ESTIMATE refers to a single value that best determines the proposed parameter value of the population POINT ESTIMATION the process of finding the point estimate involves sampling and hypothesis testing

7. Estimators Measure Parameter Statistic Mean μ Variance Standard Deviation σ s Measure Parameter Statistic Mean μ Variance Standard Deviation σ s Estimators are the measures or functions that are used to obtained the estimates.

8. Properties of a Good Estimator UNBIASEDNESS When the expectation of all estimates taken from samples are equal to the parameter being estimated. CONSISTENCY When the estimate produced a relatively small standard error/deviation (possible amount of error of estimating a population parameter) EFFICIENCY When the estimate gives the smallest variance or spread.

9. Point Estimation for the Population Mean and Variance

10. Example 6.1, p. 126 A concert for a cause is attended by individuals of different age groups. Given in the table below are the ages of randomly selected audience of the concert. Compute the point estimates if the randomly selected audience in the right side and left side are being considered.

11. Example 6.1, p. 126 Left Side 18 18 19 20 25 Right Side 17 18 19 20 24 Compute for the mean and standard deviation. Left Side Right Side Combined

12. Left Side 18 18 19 20 25 Right Side 17 18 19 20 24 a. Compute the mean.   The mean of the sample on the left side is 20 years old.   The mean of the sample on the right side is 19.6 years old.   or   The mean of the combined samples is 19.8 years old.

13. c. Compute the standard deviation.   The standard deviation of the sample on the left side is 2.92. 18 -2 4 18 -2 4 19 -1 1 20 25 5 25 18 -2 4 18 -2 4 19 -1 1 20 25 5 25 Left:   →  

14. c. Compute the standard deviation.   The standard deviation of the sample on the right side is 2.70. 17 -2.6 6.76 18 -1.6 2.56 19 -0.6 0.36 20 0.4 0.16 24 4.4 19.36 17 -2.6 6.76 18 -1.6 2.56 19 -0.6 0.36 20 0.4 0.16 24 4.4 19.36 Right:   →  

15. d. Compute the standard deviation of the combined groups. The standard deviation of the combined samples is 2.66. 18 -1.8 3.24 18 -1.8 3.24 19 -0.8 0.64 20 0.2 0.04 25 5.2 27.04 17 -2.8 7.84 18 -1.8 3.24 19 -0.8 0.64 20 0.2 0.04 24 4.2 17.64 18 -1.8 3.24 18 -1.8 3.24 19 -0.8 0.64 20 0.2 0.04 25 5.2 27.04 17 -2.8 7.84 18 -1.8 3.24 19 -0.8 0.64 20 0.2 0.04 24 4.2 17.64 Combined:     →  

16. Enhancement (Seatwork): Go over the properties of a good estimator and relate them to the obtained point estimates in Example 6.1. Which is the best estimator of the ages of the audience: the point estimate of sample from the left, from the right, or the combined samples? Why?