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# Statistical Inference

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### What is the primary goal of statistical inference?

To make conclusions or decisions about a population based on a sample of data

Estimation

P-value

### What is the maximum probability of rejecting the null hypothesis when it is true?

<p>Significance level</p> Signup and view all the answers

### What represents the range of values within which the population parameter is likely to lie?

<p>Width of the interval</p> Signup and view all the answers

## Study Notes

### Statistical Inference

#### Definition

• The process of making conclusions or decisions about a population based on a sample of data
• Involves using statistical methods to make inferences about a population parameter

#### Types of Statistical Inference

• Estimation: making an educated guess about a population parameter based on a sample statistic
• Hypothesis Testing: testing a hypothesis about a population parameter based on a sample statistic

#### Estimation

• Point Estimation: estimating a population parameter with a single value
• Interval Estimation: estimating a population parameter with a range of values (confidence interval)

#### Hypothesis Testing

• Null Hypothesis (H0): a statement of no effect or no difference
• Alternative Hypothesis (H1): a statement of an effect or difference
• Test Statistic: a statistic used to decide between H0 and H1
• P-Value: the probability of observing a test statistic at least as extreme as the one observed, assuming H0 is true
• Significance Level (α): the maximum probability of rejecting H0 when it is true

#### Errors in Hypothesis Testing

• Type I Error: rejecting H0 when it is true
• Type II Error: failing to reject H0 when it is false

#### Confidence Intervals

• Margin of Error: the maximum amount by which the sample statistic may differ from the population parameter
• Confidence Level: the probability that the confidence interval contains the population parameter
• Width of the Interval: the range of values within which the population parameter is likely to lie

### Statistical Inference

#### Definition and Purpose

• Statistical inference is the process of making conclusions or decisions about a population based on a sample of data
• It involves using statistical methods to make inferences about a population parameter

### Estimation

• Estimation involves making an educated guess about a population parameter based on a sample statistic
• There are two types of estimation:

### Point Estimation

• Estimating a population parameter with a single value

### Interval Estimation

• Estimating a population parameter with a range of values (confidence interval)

#### Hypothesis Testing

• Hypothesis testing involves testing a hypothesis about a population parameter based on a sample statistic
• There are two types of hypotheses:

### Null Hypothesis (H0)

• A statement of no effect or no difference

### Alternative Hypothesis (H1)

• A statement of an effect or difference
• The test statistic is used to decide between H0 and H1
• The p-value is the probability of observing a test statistic at least as extreme as the one observed, assuming H0 is true
• The significance level (α) is the maximum probability of rejecting H0 when it is true

#### Errors in Hypothesis Testing

• Type I Error:
• Rejecting H0 when it is true
• The probability of a Type I Error is α
• Type II Error:
• Failing to reject H0 when it is false
• The probability of a Type II Error is β

#### Confidence Intervals

• A confidence interval provides a range of values within which the population parameter is likely to lie
• The margin of error is the maximum amount by which the sample statistic may differ from the population parameter
• The confidence level is the probability that the confidence interval contains the population parameter
• The width of the interval is the range of values within which the population parameter is likely to lie

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## Description

Learn about the process of making conclusions about a population based on a sample of data, including estimation and hypothesis testing.

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