2.4 Statistical-Inferences

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Statistical Inferences
Understanding Data-Based Decision Making
by Jitendra Tomar
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Statistical Inference An Introduction
Definition
Estimation
Hypothesis Testing
Drawing conclusions about a population from a
sample based on statistical methods.
Used to make decisions or inferences about
population parameters by analyzing sample data.
(Point Interval) Used to estimate population
parameters using sample data.
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Types of Estimation
Point Estimation
Provides a single best estimate of an unknown
parameter, such as the sample mean being an
estimate of the population mean
Interval Estimation
Provides a range of values within which the
parameter is expected to lie, often accompanied
by a confidence level, such as 95 confidence
interval.
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Understanding Confidence Intervals
Formula
Margin of Error
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Sample Estimate Margin of Error
A value that reflects the extent of uncertainty
or variability in the sample estimate.
95 Confidence
Sample Estimate
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The statistic calculated from the sample data,
such as the sample mean or proportion
95 confident that the true population parameter
falls within the given range.
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Hypothesis Testing Basics
Null Hypothesis (H0)
Alternative Hypothesis (H1)
Significance Level (a)
Represents the default assumption that there is
no effect or difference in the population.
Represents the assumption that there is a
significant effect or difference in the
population.
A predefined threshold (commonly 0.05) that
determines the probability of rejecting the null
hypothesis when it is true.
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Steps in Hypothesis Testing
State Hypotheses
State H0 and H1, clearly defining the assumptions.
Choose a
Choose significance level (a), which controls the
risk of making a Type I error.
Select Test
Select appropriate test (z-test, t-test,
chi-square test, etc.) based on data
characteristics.
Compute Statistic
Compute test statistic using relevant formulas
and sample data.
Draw Conclusion
Reject or fail to reject H0 based on test results.
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Understanding Types of Errors
Type I Error
Type II Error
(False Positive) Occurs when we reject H0 when it
is actually true, leading to a false claim of
significance.
(False Negative) Occurs when we fail to reject H0
when it is actually false, leading to a missed
detection of a real effect.
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Practical Applications of Inference
A/B Testing
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Companies use hypothesis testing to evaluate
different marketing strategies and choose the
most effective one.
Medical Trials
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Clinical trials rely on statistical inference to
determine if new treatments are significantly
better than existing ones.
Quality Control
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Companies use hypothesis testing to evaluate
different marketing strategies and choose the
most effective one.
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Conclusion Key Takeaways
Data-Driven Decisions
Make decisions accurately.
Reliable Predictions
Statistical inference validates hypotheses.
Confidence
Apply statistical inference confidently.
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Next Steps in Statistical Inference
Practice Problems
Advanced Topics
Real-World Projects
Hone your skills.
Explore regression and more.
Apply knowledge to data.