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Questions and Answers
What is a hypothesis?
What is a hypothesis?
A hypothesis is a tentative statement that explains facts about a situation based on available evidence.
What is the purpose of hypothesis testing?
What is the purpose of hypothesis testing?
Hypothesis testing is a statistical procedure used to resolve a hypothesis.
What are the two main types of hypotheses?
What are the two main types of hypotheses?
What is the difference between a null hypothesis and an alternative hypothesis?
What is the difference between a null hypothesis and an alternative hypothesis?
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Explain the concept of a rejection region in hypothesis testing.
Explain the concept of a rejection region in hypothesis testing.
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A directional test involves a comparison where the alternative hypothesis is expressed as 'less than' (<) or 'greater than' (>).
A directional test involves a comparison where the alternative hypothesis is expressed as 'less than' (<) or 'greater than' (>).
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A nondirectional test involves a comparison where the alternative hypothesis is expressed as 'not equal to' (≠).
A nondirectional test involves a comparison where the alternative hypothesis is expressed as 'not equal to' (≠).
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What is a Type I error? (Select all that apply)
What is a Type I error? (Select all that apply)
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Study Notes
Hypothesis Testing
- Hypotheses are tentative statements explaining facts based on available evidence.
- Hypothesis testing is a statistical procedure to validate a hypothesis.
- A statistical hypothesis is a statement about a population parameter.
- Null hypothesis (H₀) states no difference or no relationship.
- Alternative hypothesis (Hₐ) states a difference or a relationship.
Two Kinds of Hypotheses
- Null Hypothesis (H₀): A statement that there is no difference between a parameter and a specific value.
- Alternative Hypothesis (Hₐ): A statement that there exists a difference between a parameter and a specific value, or the negation of the null hypothesis.
Types of Tests and Rejection Regions
- Directional test (One-tailed): A test with an alternative hypothesis expressing less than (<) or greater than (>) is directional. Rejection region is on one side of the distribution.
- Nondirectional test (Two-tailed): A test with an alternative hypothesis expressed as not equal to (≠) is non-directional. Rejection region is on both sides of the distribution.
Types of Errors
- Type I error (α error): Rejecting the null hypothesis when it's true.
- Type II error (β error): Accepting the null hypothesis when it's false.
Level of Significance
- The probability of committing a Type I error. It's symbolized by α (alpha).
Parameters and Their Symbols
- Mean (μ): The average of outcomes in a process or experiment.
- Variance (σ²): A measure of variability of a data set.
- Standard deviation (σ): The square root of variance, indicating average distance of observed values from the mean.
Test Statistic Formulas (z-test/t-test)
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Z-test formula is used when the population variance is known and the sample size (n) is greater than or equal to 30. Z = (X - μ) / (σ / √n) where: X = sample mean μ = population mean σ = population standard deviation n = sample size
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t-test formula is used when the population variance is unknown with sample size less than 30. t = (X - μ) / (s / √n) where: X = sample mean μ = population mean s = sample standard deviation n = sample size df = n - 1
Scatter Plots
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Scatter plots are diagrams showing the relationships between two sets of data. Plotting data points on a graph displays a trend.
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Variables are labeled with independent (X-axis), and dependent (Y-axis), values.
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A scatter plot can show correlation between variables.
Pearson's Correlation Coefficient (r)
- r: A numerical value from -1 to +1 representing the strength and direction of correlation between variables. Values close to ±1 indicate strong correlation.
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Description
This quiz explores the fundamentals of hypothesis testing, including the definitions and differences between null and alternative hypotheses. It also covers types of tests and rejection regions in statistical analysis. Test your knowledge on the critical concepts of hypothesis testing.
