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 hours)
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, XX = 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 (s2) =
(𝑋 − 𝑋)2
𝑛 −1
Compute for the standard deviation (s) =
(𝑋 − 𝑋)2
𝑛 −1
where Σ = summation
X = column mean
X = overall mean
n = number of cases