PHILIPPINE STATISTCICS UNIT~2.POWER POINT T SAMPLE

SAMPLE

1. CONFIDENCE INTERVALS FOR THE
POPULATION MEAN WHEN IS
UNKNOWN


2. Lesson Objectives
At the end of this lesson, you are expected to:
•identify the appropriate distribution when the
population σ is unknown;
•understand the t-distribution;
•state the difference between a z-distribution and a
t-distribution; and
•identify the confifidence coeffifficients for
computing t from the t-Table.

3. Pre-Assessment

4. Lesson Introduction
Aldrei wants to know if cooperative grouping is an effective strategy in
improving the mathematics performance of Grade 7 students. Twenty
students were included in the experimental group while another 20
students were included in the control group. The mean achievement
score of the students in the experimental group was 82.5 with a
standard deviation of 3 while the mean of the students in the control
group was 80 with a standard deviation of 6. The two groups come from
normally distributed populations. The confidence level adopted was
95%.
•What is the estimate of the population mean where the
experimental group comes from?
___________________________
•What is the estimate of the population mean where the control
group comes from? ___________________________
•Express your confidence as percentage. ____________________

5. Discussion Points
Assumptions in Computing for the Population
Mean When σ is Unknown
When n ≥ 30, and σ is unknown, the sample
standard deviation scan be substituted for σ.
However, the following assumptions should be
met.
•The sample is a random sample.
•Either n ≥ 30 or the population is normally
distributed when n < 30.

6. Discussion Points
General expression for the confidence interval when σ is unknown
The distribution of values is called t-distribution

Xt
s
n







7. Discussion Points
Degrees of Freedom

•The degrees of freedom, denoted by df, are
the number of values that are free to vary
after a sample statistic has been computed
• Indicate the specific curve to use when a
distribution consists of a family of curves.

8. Discussion Points
Formula for computing the confidence interval
using the t-distribution


Xt
s
n






Xt
s
n







9. Discussion Points

10. Example 1
An admission officer of an educational institution wants
to know the mean age of all entering mathematics
majors. He computed a mean age of 18 years and a
standard deviation of 1.2 years on a random sample of
25 entering mathematics majors purportedly coming
from a normally distributed population.
With 99% confidence, find the point estimate and the
interval estimate of the population mean.

11. Solution
Point Estimate

12. Solution
99% Confidence Interval

13. Solution
99% Confidence Interval

14. Exercises
1.Using the t-table, give the confidence
coefficients for each of the following:
 n = 12, 95% confidence
 n = 15, 95% confidence
 n = 21, 99% confidence
 n = 23, 95% confidence
 n = 25, 99% confidence

15. Exercises
2.The mean scores of a random sample of 17 students
who took a special test is 83.5. If the standard
deviation of the scores is 4.1, and the sample comes
from an approximately normal population, find the
point and the interval estimates of the population
mean adopting a confidence level of 95%.
3.The mean age of 20 youth volunteers in a community
project is 17.5 years with a standard deviation of 2
years. If the sample comes from an approximately
normal distribution, what are the point and the interval
estimates of the population mean? Use 99%
confidence level.

16. Exercises
4.The average weight of 25 chocolate bars
selected from a normally distributed
population is 200 g with a standard
deviation of 10 g. Find the point and the
interval estimates using 95% confidence
level.

17. Summary
General expression for the confidence interval when σ is unknown
The distribution of values is called t-distribution

Xt
s
n







18. Summary