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Questions and Answers
The goal of hypothesis testing in statistics is to prove the null hypothesis.
The goal of hypothesis testing in statistics is to prove the null hypothesis.
False (B)
The alternative hypothesis often suggests that a relationship or change exists.
The alternative hypothesis often suggests that a relationship or change exists.
True (A)
The significance level, denoted by α, represents the probability of a Type II error, which is accepting the null hypothesis when it is actually false.
The significance level, denoted by α, represents the probability of a Type II error, which is accepting the null hypothesis when it is actually false.
False (B)
A test statistic is a value calculated from the sample data used to evaluate the hypothesis.
A test statistic is a value calculated from the sample data used to evaluate the hypothesis.
A t-test, z-test, and chi-square test are all examples of specific statistical tests used in hypothesis testing.
A t-test, z-test, and chi-square test are all examples of specific statistical tests used in hypothesis testing.
The p-value represents the probability of obtaining the observed results or a more extreme result if the alternative hypothesis is true.
The p-value represents the probability of obtaining the observed results or a more extreme result if the alternative hypothesis is true.
If the p-value is less than the significance level, we reject the null hypothesis.
If the p-value is less than the significance level, we reject the null hypothesis.
Hypothesis testing is only used in scientific research and not in everyday decision-making.
Hypothesis testing is only used in scientific research and not in everyday decision-making.
The null hypothesis represents the default assumption and states that there is no effect.
The null hypothesis represents the default assumption and states that there is no effect.
If the calculated p-value is greater than the significance level ($\alpha$), the null hypothesis should be rejected.
If the calculated p-value is greater than the significance level ($\alpha$), the null hypothesis should be rejected.
The alternative hypothesis may reflect a claim that researchers aim to support.
The alternative hypothesis may reflect a claim that researchers aim to support.
Only one-tailed tests are used when setting up alternative hypotheses.
Only one-tailed tests are used when setting up alternative hypotheses.
The conclusion drawn from hypothesis testing should include the context of the research question.
The conclusion drawn from hypothesis testing should include the context of the research question.
Hypothesis testing is not important in making data-driven decisions.
Hypothesis testing is not important in making data-driven decisions.
The critical value method involves comparing the test statistic to a value from statistical tables.
The critical value method involves comparing the test statistic to a value from statistical tables.
Flashcards
Hypothesis Testing
Hypothesis Testing
A statistical method to make decisions about a population based on sample data.
Null Hypothesis (H0)
Null Hypothesis (H0)
A default assumption that there is no effect or relationship in the population.
Alternative Hypothesis (Ha)
Alternative Hypothesis (Ha)
A statement that contradicts the null hypothesis, suggesting an effect exists.
Significance Level (α)
Significance Level (α)
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Test Statistic
Test Statistic
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P-Value
P-Value
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Procedure for Testing Hypothesis
Procedure for Testing Hypothesis
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Collect and Summarize Data
Collect and Summarize Data
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Critical Value Method
Critical Value Method
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P-Value Method
P-Value Method
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Null Hypothesis (H₀)
Null Hypothesis (H₀)
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Alternative Hypothesis (Hₐ)
Alternative Hypothesis (Hₐ)
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Decision Rule
Decision Rule
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One-tailed vs Two-tailed Test
One-tailed vs Two-tailed Test
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Conclusion in Hypothesis Testing
Conclusion in Hypothesis Testing
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Study Notes
Introduction to Hypothesis Testing
- Hypothesis testing is a statistical method to make decisions about population characteristics from sample data.
- It helps determine if evidence supports a certain population condition.
- Aims to test assumptions about population parameters (mean, proportion, etc).
- Enables conclusions and informed decisions based on data analysis.
- Key terms: Hypothesis, Null Hypothesis (H₀), Alternative Hypothesis (Hₐ), Significance Level (α), Test Statistic, P-value.
Procedure for Hypothesis Testing
- Define the Problem: Clearly state the research question.
- Formulate Hypotheses:
- Null Hypothesis (H₀): Assumes no effect, difference, or relationship.
- Alternative Hypothesis (Hₐ): Contradicts H₀, representing the tested claim.
- Select Significance Level (α): Decide on the acceptable risk of a Type I error (rejecting H₀ when true). Commonly 0.05 or 5%.
- Choose Appropriate Statistical Test: Select a test based on data type and research goal (t-test, z-test, chi-square, ANOVA).
- Collect and Summarize Data: Gather the sample data and calculate relevant statistics (mean, standard deviation).
- Calculate Test Statistic: Compute the test statistic using the chosen test and sample data.
- Determine Critical Value or P-Value: Compare the test statistic to a critical value or the p-value to the significance level.
- Make a Decision: Reject H₀ if the p-value ≤ α; otherwise, fail to reject H₀.
- Draw a Conclusion: Interpret the outcome in the context of the research question.
Setting Hypotheses (Null and Alternative)
- Null Hypothesis (H₀): The default assumption, positing no effect, difference, or relationship.
- Examples: H₀: μ = μ₀ (population mean equals a value), H₀: p = p₀ (population proportion equals a value)
- Alternative Hypothesis (Hₐ): Contradicts H₀, stating the researcher's claim.
- Can be one-tailed (e.g., greater than, less than) or two-tailed (not equal to).
- Examples: Hₐ: μ ≠ μ₀ (two-tailed), Hₐ: μ > μ₀ or Hₐ: μ < μ₀ (one-tailed)
- Can be one-tailed (e.g., greater than, less than) or two-tailed (not equal to).
- Example: Research question: Does a new drug reduce blood pressure more than a current drug?
- H₀: The new drug is not more effective ((\mu_{\text{new}} \le \mu_{\text{existing}})).
- Hₐ: The new drug is more effective ((\mu_{\text{new}} > \mu_{\text{existing}})).
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