Point and Interval Estimation when the population distribution is not
- The process of finding a single value, called normal
point estimate, from a random sample of 3. Different samples of size n taken from the
the population, to approximate a same population, produce different results.
population parameter. In the case of a sample mean x ̅, the result
✰ sample mean is the point estimate of is affected by the presence of
the population mean outliers.These are the data that are
✰ s²(sample variance) is the point
numerically too far from the rest of the
estimate of σ2 (population variance)
data.
Example 1:
The sample mean is 46.72 and the population Example 3:
mean is 47.01. Consider the population consisting of values
(5,3,4,6,7). Find the population mean.
Answer: the point estimate is the single value
46.72
Observation x
!! Note: 1 5
A good point estimate is one that is unbiased. If 2 3
the random sampling was done in the collection
of a set of data, and a sample mean is computed 3 4
out of these data to approach the population 4 6
mean, then the point estimate is a good point
5 7
estimate.
∑x=25
Example 2:
A teacher wanted to determine the average μ=(∑x)/N
height of Grade 9 student in their school. What he =25/5
did was to go to one of the 8 sections in Grade 9 =5
and then took their heights. He computed for the
mean height of the students and got 165 cm. Confidence Interval
- Instead of using the point estimate, it is
Question: Is 165 cm a good point estimate?
better to approximate the population
Why?
parameter by determining a range of
Answer: 165 cm is not a good point estimate of values within which the population mean
the population. The teacher should have is most likely to be located.
randomly selected the members of his sample - This range of values is called the
from the entire population using any of the 4 confidence interval.
types of Random Sampling. - refers to the probability that the
confidence interval contains the true
!! Remember:
population parameter. Its value is
1. A researcher should not expect the point
estimate to be exactly equal to the confidence level=(1-α)100%
population parameter. However, any point where α=probability that the confidence interval
estimate used should be as close as does not contain the true population parameter.
possible to the true parameter.
2. Data should be carefully collected.
Sampling should be done at random and !! Remember:
the sample size should be large especially 1. The confidence levels of 90%, 95%, and 99%
are usually chosen.
- The process of finding a single value, called normal
point estimate, from a random sample of 3. Different samples of size n taken from the
the population, to approximate a same population, produce different results.
population parameter. In the case of a sample mean x ̅, the result
✰ sample mean is the point estimate of is affected by the presence of
the population mean outliers.These are the data that are
✰ s²(sample variance) is the point
numerically too far from the rest of the
estimate of σ2 (population variance)
data.
Example 1:
The sample mean is 46.72 and the population Example 3:
mean is 47.01. Consider the population consisting of values
(5,3,4,6,7). Find the population mean.
Answer: the point estimate is the single value
46.72
Observation x
!! Note: 1 5
A good point estimate is one that is unbiased. If 2 3
the random sampling was done in the collection
of a set of data, and a sample mean is computed 3 4
out of these data to approach the population 4 6
mean, then the point estimate is a good point
5 7
estimate.
∑x=25
Example 2:
A teacher wanted to determine the average μ=(∑x)/N
height of Grade 9 student in their school. What he =25/5
did was to go to one of the 8 sections in Grade 9 =5
and then took their heights. He computed for the
mean height of the students and got 165 cm. Confidence Interval
- Instead of using the point estimate, it is
Question: Is 165 cm a good point estimate?
better to approximate the population
Why?
parameter by determining a range of
Answer: 165 cm is not a good point estimate of values within which the population mean
the population. The teacher should have is most likely to be located.
randomly selected the members of his sample - This range of values is called the
from the entire population using any of the 4 confidence interval.
types of Random Sampling. - refers to the probability that the
confidence interval contains the true
!! Remember:
population parameter. Its value is
1. A researcher should not expect the point
estimate to be exactly equal to the confidence level=(1-α)100%
population parameter. However, any point where α=probability that the confidence interval
estimate used should be as close as does not contain the true population parameter.
possible to the true parameter.
2. Data should be carefully collected.
Sampling should be done at random and !! Remember:
the sample size should be large especially 1. The confidence levels of 90%, 95%, and 99%
are usually chosen.
