95% Confidence Interval
Based on the Washington data from the population, a range of values known as the 95% confidence interval for the population’s mean and variance is created. It offers some ambiguity regarding the actual population mean and variance values.
95% Confidence Interval for the Mean
Formula: Confidence Interval = Sample Mean ± Margin of Error
The sample size, sample standard deviation, and selected confidence level (in this example, 95%), all influence the margin of error.
If the population standard deviation is known (often denoted as σ), we can use the Z-distribution and the formula:
Margin of Error (Z-distribution)
Where:
Z is the critical value corresponding to a 95% confidence level (usually 1.96 for 95% confidence).
σ is the population standard deviation.
n is the sample size.
95% Confidence Interval for the Variance
To construct a 95% confidence interval for the population variance (σ^2), we use the Chi-squared distribution.
The formula for the confidence interval is
Where
n is the sample size.
s^2 is the sample variance.
χ^2_upper and χ^2_lower are the critical values of the Chi-squared distribution corresponding to the upper and lower tail
Moving towards the project
While plotting the graph for all 7 different types of race wrt to age and calculating the 95% CI
This is how it looked like with respect to mean age:
95% CI for mean age of Asian race: (34.102561714042324, 38.17163183434478)
95% CI for mean age of Black race: (32.2672685325096, 33.36063844423459)
95% CI for mean age of Hispanic race: (33.025105503719516, 34.26648662508191)
95% CI for mean age of Native American race: (31.171378988317556, 35.06775144646505)
95% CI for mean age of Other race: (28.60618586384799, 38.69381413615201)
95% CI for mean age of Unknown race: (39.27258057718045, 41.59356115510302)
95% CI for mean age of White race: (39.67225966058736, 40.5853739271989)
with respect to age variance:
95% CI for age variance of Asian race: (-40.85984853099225, 308.09024454462985)
95% CI for age variance of Black race: (-9.30460757975456, 270.24488620549687)
95% CI for age variance of Hispanic race: (-9.912485515846711, 234.15910188380138)
95% CI for age variance of Native American race: (-33.487313303846264, 215.28258325129013)
95% CI for age variance of Other race: (-150.1015458360546, 415.0015458360547)
95% CI for age variance of Unknown race: (-26.69241274796164, 471.92870773790173)
95% CI for age variance of White race: (-8.759132313413176, 349.9572418892791)
And the graph of Q-Q plot wrt to age distribution
These are just random figures posted from the lot and also go the information of stats age wrt to their race
Race: Unknown
Median: 38.00
Mean: 40.43
Standard Deviation: 14.92
Variance: 222.62
Skewness: 0.67
Kurtosis: 2.9363
Race: Native American
Median: 32.00
Mean: 33.12
Standard Deviation: 9.53
Variance: 90.90
Skewness: 0.58
Kurtosis: 2.8620
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