https://github.com/anas436/introduction-to-confidence-intervals-in-python
https://github.com/anas436/introduction-to-confidence-intervals-in-python
confidence-intervals inferential-statistics jupyterlab numpy pandas python3 statsmodels
Last synced: 7 months ago
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- Host: GitHub
- URL: https://github.com/anas436/introduction-to-confidence-intervals-in-python
- Owner: Anas436
- Created: 2022-10-29T13:18:28.000Z (over 3 years ago)
- Default Branch: main
- Last Pushed: 2022-10-29T13:22:17.000Z (over 3 years ago)
- Last Synced: 2025-03-27T10:48:07.788Z (11 months ago)
- Topics: confidence-intervals, inferential-statistics, jupyterlab, numpy, pandas, python3, statsmodels
- Language: Jupyter Notebook
- Homepage:
- Size: 5.86 KB
- Stars: 0
- Watchers: 2
- Forks: 0
- Open Issues: 0
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Metadata Files:
- Readme: README.md
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README
# Introduction-to-Confidence-Intervals-in-Python
## Statistical Inference with Confidence Intervals
Throughout week 2, we have explored the concept of confidence intervals, how to calculate them, interpret them, and what confidence really means.
__In this tutorial, we're going to review how to calculate confidence intervals of population proportions and means.__
To begin, let's go over some of the material from this week and why confidence intervals are useful tools when deriving insights from data.
### Why Confidence Intervals?
Confidence intervals are a calculated range or boundary around a parameter or a statistic that is supported mathematically with a certain level of confidence. For example, in the lecture, we estimated, with 95% confidence, that the population proportion of parents with a toddler that use a car seat for all travel with their toddler was somewhere between 82.2% and 87.7%.
This is *__different__* than having a 95% probability that the true population proportion is within our confidence interval.
Essentially, if we were to repeat this process, 95% of our calculated confidence intervals would contain the true proportion.
### How are Confidence Intervals Calculated?
Our equation for calculating confidence intervals is as follows:
$$Best\ Estimate \pm Margin\ of\ Error$$
Where the *Best Estimate* is the **observed population proportion or mean** and the *Margin of Error* is the **t-multiplier**.
The t-multiplier is calculated based on the degrees of freedom and desired confidence level. For samples with more than 30 observations and a confidence level of 95%, the t-multiplier is 1.96
The equation to create a 95% confidence interval can also be shown as:
$$Population\ Proportion\ or\ Mean\ \pm (t-multiplier *\ Standard\ Error)$$
Lastly, the Standard Error is calculated differenly for population proportion and mean:
$$Standard\ Error \ for\ Population\ Proportion = \sqrt{\frac{Population\ Proportion * (1 - Population\ Proportion)}{Number\ Of\ Observations}}$$
$$Standard\ Error \ for\ Mean = \frac{Standard\ Deviation}{\sqrt{Number\ Of\ Observations}}$$
Let's replicate the car seat example from lecture: