Estimation of Parameters
Objectives
Start
Story
Pop and Samp Parameters
Empirical Estimation
Confidence Interval
Practice
Summary
Story
Population and Sample Parameters
How can we know something about a huge group (a Population) without checking every single member?
We use a small, representative part (a Sample) and a process called Estimation
A random sample of town habitants.
Whole population of people in a town
Let's see some examples:
Example 2: A sample parameter Number of 12th graders in a selected random town within Florida (like Tampa F.L.).
Example 1: A population parameter Average number of 12th graders in Florida (for all years).
N=12540
n=3520
Some Common Population and Sample Characteristics
SAMPLE (n DATA)
population(N data)
MEAN
sTANDARD DEVIATION
PROPORTION
Let's see some examples:
Example:
A national poll wants to estimate the percentage of U.S. adults who own a cryptocurrency.
If 150 of them own crypto, estimate the proportion of crypto owners.
Could it be valid for the whole U.S?Why?
The poll surveys a random sample of n=1000 adults.
Empirical Estimation
Empirical Rule
Certain percentage of the data is between the mean and the standard deviation.
68% of data within μ ± σ
95% of data within μ ± 2σ
99.7% of data within μ ± 3σ
Let's see some examples:
Example:
The average annual salary in a city in US Dollars, USD) and its standard deviation are shown.
Let's find the salary range within the average for 68% of people :
68% of data is in between μ -1σ and μ +1σ
σ = $5,000
μ = $60,000
Assume salaries are normally distributed.
$55,000 - $65,000
Confidence Interval
What is the Confidence Interval (CI)?
A Confidence Interval provides a range of values that is likely to contain the true population parameter.
Form of the interval:
Where:
Statistic±
Margin of Error
Margin of Error
Critical Value
Standard Error
Let's see some examples:
Example:
If a business sells a product for 1000¥ (Japanese Yen) with a 95% CI and a standard error of 2.5¥
What is the profit margin of the business?
From 989¥ to 1,011¥
1000¥
Practice
Try it by yourself:
Try it by yourself:
Try it by yourself:
Try it by yourself:
Summary: Estimation of Parameters
confidence interval
sample parameters
Great job!
See you next time
Welcome 6th graders!
A journey soon begin through Social Science experiences!
6TH-INTRODUCTIONTORATIONALNUMBERS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0
MA.912.DP.2 Solve problems involving univariate and bivariate numerical data. MA.912.DP.2.3 Estimate population percentages from data that has been fit to the normal distribution. ELD.K12.ELL.MA: Language of Mathematics ELD.K12.ELL.MA.1 English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. MA.K12.MTR.7: Apply mathematics to real-world contexts. MA.K12.MTR.7.1 Apply mathematics to real-world contexts.
MATERIAL
It is highly advised to have:
- Grid paper.
- Pencils of different colors.
- Eraser.
- A rule.
- A calculator.
- Geogebra installed on your phone/tablet/computer (or use online version).
WEEK 29-ESTIMATION-OF-PARAMETERS
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Transcript
Estimation of Parameters
Objectives
Start
Story
Pop and Samp Parameters
Empirical Estimation
Confidence Interval
Practice
Summary
Story
Population and Sample Parameters
How can we know something about a huge group (a Population) without checking every single member?
We use a small, representative part (a Sample) and a process called Estimation
A random sample of town habitants.
Whole population of people in a town
Let's see some examples:
Example 2: A sample parameter Number of 12th graders in a selected random town within Florida (like Tampa F.L.).
Example 1: A population parameter Average number of 12th graders in Florida (for all years).
N=12540
n=3520
Some Common Population and Sample Characteristics
SAMPLE (n DATA)
population(N data)
MEAN
sTANDARD DEVIATION
PROPORTION
Let's see some examples:
Example: A national poll wants to estimate the percentage of U.S. adults who own a cryptocurrency.
If 150 of them own crypto, estimate the proportion of crypto owners.
Could it be valid for the whole U.S?Why?
The poll surveys a random sample of n=1000 adults.
Empirical Estimation
Empirical Rule
Certain percentage of the data is between the mean and the standard deviation.
68% of data within μ ± σ
95% of data within μ ± 2σ
99.7% of data within μ ± 3σ
Let's see some examples:
Example: The average annual salary in a city in US Dollars, USD) and its standard deviation are shown.
Let's find the salary range within the average for 68% of people :
68% of data is in between μ -1σ and μ +1σ
σ = $5,000
μ = $60,000
Assume salaries are normally distributed.
$55,000 - $65,000
Confidence Interval
What is the Confidence Interval (CI)?
A Confidence Interval provides a range of values that is likely to contain the true population parameter.
Form of the interval:
Where:
Statistic±
Margin of Error
Margin of Error
Critical Value
Standard Error
Let's see some examples:
Example: If a business sells a product for 1000¥ (Japanese Yen) with a 95% CI and a standard error of 2.5¥
What is the profit margin of the business?
From 989¥ to 1,011¥
1000¥
Practice
Try it by yourself:
Try it by yourself:
Try it by yourself:
Try it by yourself:
Summary: Estimation of Parameters
confidence interval
sample parameters
Great job!
See you next time
Welcome 6th graders!
A journey soon begin through Social Science experiences!
6TH-INTRODUCTIONTORATIONALNUMBERS-EN © 2024 by CASURID is licensed under CC BY-NC-ND 4.0
MA.912.DP.2 Solve problems involving univariate and bivariate numerical data. MA.912.DP.2.3 Estimate population percentages from data that has been fit to the normal distribution. ELD.K12.ELL.MA: Language of Mathematics ELD.K12.ELL.MA.1 English language learners communicate information, ideas and concepts necessary for academic success in the content area of Mathematics. MA.K12.MTR.7: Apply mathematics to real-world contexts. MA.K12.MTR.7.1 Apply mathematics to real-world contexts.
MATERIAL
It is highly advised to have: