Chapter 4 estimation of parameters

Estimation of Parameters

1. Chapter 4 Estimation of Parameters Mr. Anthony F. Balatar Jr. Subject Instructor

2. Computing The Point Estimate Of A Population Mean INTRODUCTORY TASK Starting April 1 – 14, 2020, make a record that shows your sleep hours during the Enhanced Community Quarantine. Please be guided of the table below. Use MS Excel. Date Sleep Time Wake Up Time Time Consumed (in hour s) April 1, 2020 April 2, 2020 . . April 14, 2020 AVERAGE SLEEPING HOURS _____ hours

3. Computing The Point Estimate Of A Population Mean The arithmetic average computed from the table is also known as mean . Each student constitutes a sample. If we repeat the activity to, say, ten random students, then we obtain ten arithmetic averages or means. Suppose we proceed to compute the mean of the means for all ten (10) students. The final result is a number that is called point estimate of the mean μ of the population where the samples come from.

4. Computing The Point Estimate Of A Population Mean In symbols, X X = μ . This expression is read as “the mean of the means is equal to the population mean μ (read myu ).” We can estimate population parameters from sample values. In Statistics, sample measures, such as the sample means and standard deviations, are used to estimate population values.

5. Computing The Point Estimate Of A Population Mean An estimate is a value or a range of values that approximate a parameter. It is based on sample statistics computed from sample data. Estimation is the process of determining parameter values.

6. Computing The Point Estimate Of A Population Mean Illustrative Example . Susan, a TLE researcher, looked at the average time (in minutes) it takes a random sample of customers to be served in a restaurant. From 40 customers, the following information was obtained. What is the average wait time? 8 8 10 18 10 13 8 10 8 10 12 10 16 16 12 15 12 12 9 15 10 20 20 12 10 10 16 10 18 12 15 12 15 14 15 16 15 12 8 8

7. Computing The Point Estimate Of A Population Mean Illustrative Example . Mr. Santiago’s company sells bottled coconut juice. He claims that a bottle contain 500 mL of such juice. A consumer group wanted to know if his claim is true. They took six random samples of 10 such bottles and obtained the capacity, in mL, of each bottle. The result is shown as follows:

8. Computing The Point Estimate Of A Population Mean Compute for the mean in each sample. Compute for the point estimate of the population mean. Sample 1 500 498 497 503 499 497 497 497 497 495 Sample 2 500 500 495 494 498 500 500 500 500 497 Sample 3 497 497 502 496 497 497 497 497 497 495 Sample 4 501 495 500 497 497 500 500 495 497 497 Sample 5 502 497 497 499 496 497 497 499 500 500 Sample 6 496 497 496 495 497 497 500 500 496 497

9. Computing The Point Estimate Of A Population Mean Compute for the mean in each sample. Compute for the point estimate of the population mean. Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 Sample 9 Sample 10 500 498 497 503 499 497 497 497 497 495 500 500 495 494 498 500 500 500 500 497 497 497 502 496 497 497 497 497 497 495 501 495 500 497 497 500 500 495 497 497 502 497 497 499 496 497 497 499 500 500 496 497 496 495 497 497 500 500 496 497

10. Computing The Point Estimate Of A Population Mean Compute for the variance (s 2 ) = Compute for the standard deviation (s) = where Σ = summation X = column mean X = overall mean n = number of cases