For Statistics and Probability, Grade XI

1. ESTIMATION

4. Estimation
the process of using
sample data to calculate a
number that can be used to
represent an unknown
population parameter.

5. Point Estimation
a single value estimate for
a population parameter

6. Interval
Estimation
a range of values used to
estimate the population
parameter

7. Sampling Error
the difference between
the point estimate and the
actual value

8. Margin of Error
the maximum error of
estimate
𝐸 = (𝑧 𝛼
2
)(𝜎𝑥)
𝐸 = (𝑧 𝛼
2
)(
𝜎𝑥
√𝑛
)
sample standard
deviation
population standard
deviation

9. REMINDER
For n> 30, the sample standard
deviation is also the population
standard deviation. That means, even if
the given is a sample SD, we use the
second formula if n>30.

10. EXAMPLE 1
The principal of a SHS wants to
know the English proficiency of all
students in his high school. Instead of
administering an examination to all
students, he decided to take a random
sample of 60 students. Given a 95%
level of confidence, and a population
standard deviation of 1.25, compute
the margin of error.

11. EXAMPLE 1
𝐸 = (𝑧 𝛼
2
)(
𝜎𝑥
√𝑛
)
𝐸 = (1.960)(
1.25
√60
)
𝐸 = 0.3163

12. EXAMPLE 2
A random sample of 40 daily
earnings (in peso) of a retail store is
generated. The sample mean is 431.5
pesos and the SD is 153.44. At 99%
confidence level, find the margin of
error E for the estimation of the mean
daily earnings of the store.

13. EXAMPLE 2
𝐸 = (𝑧 𝛼
2
)(
𝜎𝑥
√𝑛
)
𝐸 = (2.576)(
153.44
√40
)
𝐸 = 62.496