The document discusses the concepts of point and interval estimates in statistics, detailing how population parameters can be estimated from sample data. It explains two methods for calculating interval estimates: one when the population standard deviation is known, and another using the Student’s t-distribution when it is unknown. Additionally, the document includes examples and step-by-step procedures for finding point and interval estimates based on given sample data.

2. ne what is:
meter
mate
rentiate
nt estimate
erval
e
ective
:

3. - a numerica
characteristic
population, a
from a statisti
sample.
Parameter

4. Ex.
1. A number of students in CKC
2. A number of population in Brgy.
Matobato
Parameter

5. ue, or range
alues, that
roximates
population
Estimate

6. 2 Types
Point Estimate
• It is a specific
numerical value of a
population parameter
• The sample mean 𝑋 is
the best point
estimate of a
population mean.
Interval Estimate
• Also called as
confidence interval, a
range values used to
estimate a parameter.
This estimate may or
may not contain the
true parameter value.

7. Point Estimate
Ex.
Jacky wanted to know
the average students
in statistics. She
interviewed 40
students and the
results are shown on
the right.

8. Interval Estimate
• When σ is known
The confidence level of an interval estimate is the
probability that the interval estimate will contain
the true population parameter.
- How sure are we that the population
parameter is really within that we came up with.

9. Interval Estimate – 2 ways
1.) When σ is known
The confidence level of an interval estimate is the
probability that the interval estimate will contain
the true population parameter.
- How sure are we that the population
parameter is really within that we came up with.

10. Interval Estimate – 2 ways
2.) When σ is unknown
When σ is unknown, the interval estimate can be
determined using the student’s t-distribution.

11. Interval Estimate: σ is known

12. Interval Estimate
E – Margin of Error
Z - critical value/z- value
σ – population standard deviation or sigma
N – sample size

13. Interval Estimate
Lower limit
Upper Limit

14. Solve for Interval Estimate
Example:
Step 1: Determine the given values
Step 2: Determine the critical value
Step 3: Solve for the margin of error using the formula
Step 4: Solve for the Interval estimate
Procedure:

15. Solve for Interval Estimate
Example:
Given:
Sample size (n) = 100
Sample mean 𝑿 = 150
Population SD σ = 40
Confidence level = 95% = critical value: Z =1.96

16. Solve for Interval Estimate
Example:
Given:
Sample size (n) = 50
Sample mean 𝑿 = 20.5
Population SD σ = 3.7
Confidence level = 99% = critical value: Z = 2.58

17. Interval Estimate – #2 way/ method
2.) When σ is unknown
When σ is unknown, the interval estimate can be
determined using the
student’s t-distribution.

18. Interval Estimate – σ is unknown
Where; n – is the sample size

19. Interval Estimate – σ is unknown

20. Interval Estimate – σ is unknown (Example)
Step 1: Determine the given values
Step 2: Determine the degrees of freedom using the formula
and the t (using the table)
Step 3: Solve for the margin of error using the formula
Step 4: Solve for the Interval estimate
Procedure:

21. Interval Estimate – σ is unknown (Example)
Given:
Sample size (n) = 30
Sample mean 𝑿 = 5.3
Sample S = 1.1
Confidence level = 95%
Degrees of freedom = n – 1 = 30 – 1 = 29

22. Interval Estimate – σ is unknown (Example)

23. ESTIMATING SAMPLE SIZE
In order to determine the sample size we follow
the formula:
n = [
𝑍𝑎
2
σ
𝐸
]2
Where;
n = sample size
𝒁𝒂
𝟐
= Z values
E = margin error

24. ESTIMATING SAMPLE SIZE
In order to determine the sample size we follow
the formula:
n = [
𝑍𝑎
2
σ
𝐸
]2
Where;
n = sample size
𝒁𝒂
𝟐
= Z values
E = margin error

25. QUIZ !!!
1 whole sheet of paper
-YES, 1 whole

26. Direction: Solve for the Point Estimate
95 85 85 90 88 80
88 87 82 92 90 91
88 94 90 92 89 90
96 89 84 90 85 87
95 96 94 93 94 90
89 88 89 85 86 92
Mr. Gonzales wanted to know the average students in
statistics. He interviewed 36 students and the results
are shown below.

27. Direction: Solve for the Interval Estimate.
In a study of 80 junior high school students, the mean number
of hours per week that they used internet was 40 hours. It was
estimated that the population standard deviation was 2.5. What
is the 95% confidence interval for the mean time for using
internet?

28. THANK YOU !!!