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Questions and Answers
What is the primary purpose of hypothesis testing?
What is the primary purpose of hypothesis testing?
What is the null hypothesis?
What is the null hypothesis?
What is the significance level in hypothesis testing?
What is the significance level in hypothesis testing?
What is the purpose of selecting a significance level?
What is the purpose of selecting a significance level?
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What is the final step in hypothesis testing?
What is the final step in hypothesis testing?
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What is the alternative hypothesis?
What is the alternative hypothesis?
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What is the correct decision when the test statistic falls in the critical region?
What is the correct decision when the test statistic falls in the critical region?
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Which type of error occurs when the null hypothesis is rejected when it is actually true?
Which type of error occurs when the null hypothesis is rejected when it is actually true?
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Which test statistic is used for comparing multiple group means?
Which test statistic is used for comparing multiple group means?
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What is the null hypothesis assumed to be true when calculating the p-value?
What is the null hypothesis assumed to be true when calculating the p-value?
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If the p-value is less than α, what is the correct decision?
If the p-value is less than α, what is the correct decision?
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Study Notes
Hypothesis Testing
Definition
- A procedure used to test a hypothesis based on a sample of data
- Involves comparing the data to a known probability distribution or a hypothesis about the population
Types of Hypotheses
-
Null Hypothesis (H0): a statement of no effect or no difference
- Typically denoted by μ (mu) or p
- Example: "There is no significant difference in the means of two groups"
-
Alternative Hypothesis (H1): a statement of an effect or difference
- Typically denoted by μ (mu) or p
- Example: "There is a significant difference in the means of two groups"
Steps in Hypothesis Testing
- State the hypothesis: Clearly define the null and alternative hypotheses
-
Select a significance level: Choose a level of significance (α) to determine the probability of rejecting the null hypothesis when it is true (Type I error)
- Typically set at 0.05
- Collect and analyze the data: Collect a sample of data and calculate the test statistic
- Determine the critical region: Identify the region of the test statistic distribution where the null hypothesis is rejected
- Compare the test statistic to the critical value: Determine if the test statistic falls in the critical region
- Make a decision: Reject the null hypothesis if the test statistic falls in the critical region, otherwise fail to reject the null hypothesis
Errors in Hypothesis Testing
- Type I error: Rejecting the null hypothesis when it is true (α)
- Type II error: Failing to reject the null hypothesis when it is false (β)
Common Test Statistics
- t-statistic: Used for small sample sizes and unknown population standard deviation
- z-statistic: Used for large sample sizes and known population standard deviation
- F-statistic: Used for comparing multiple group means (ANOVA)
Interpretation of Results
-
p-value: The probability of observing the test statistic (or a more extreme value) assuming the null hypothesis is true
- If p-value < α, reject the null hypothesis
- If p-value ≥ α, fail to reject the null hypothesis
Hypothesis Testing
Definition
- A procedure used to test a hypothesis based on a sample of data
- Involves comparing the data to a known probability distribution or a hypothesis about the population
Hypotheses
-
Null Hypothesis (H0): a statement of no effect or no difference
- Typically denoted by μ (mu) or p
- Example: "There is no significant difference in the means of two groups"
-
Alternative Hypothesis (H1): a statement of an effect or difference
- Typically denoted by μ (mu) or p
- Example: "There is a significant difference in the means of two groups"
Steps in Hypothesis Testing
- State the hypothesis: Clearly define the null and alternative hypotheses
-
Select a significance level: Choose a level of significance (α) to determine the probability of rejecting the null hypothesis when it is true (Type I error)
- Typically set at 0.05
- Collect and analyze the data: Collect a sample of data and calculate the test statistic
- Determine the critical region: Identify the region of the test statistic distribution where the null hypothesis is rejected
- Compare the test statistic to the critical value: Determine if the test statistic falls in the critical region
- Make a decision: Reject the null hypothesis if the test statistic falls in the critical region, otherwise fail to reject the null hypothesis
Errors in Hypothesis Testing
- Type I error: Rejecting the null hypothesis when it is true (α)
- Type II error: Failing to reject the null hypothesis when it is false (β)
Common Test Statistics
- t-statistic: Used for small sample sizes and unknown population standard deviation
- z-statistic: Used for large sample sizes and known population standard deviation
- F-statistic: Used for comparing multiple group means (ANOVA)
Interpretation of Results
-
p-value: The probability of observing the test statistic (or a more extreme value) assuming the null hypothesis is true
- If p-value < α, reject the null hypothesis
- If p-value ≥ α, fail to reject the null hypothesis
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Description
Learn about hypothesis testing, a procedure used to test a hypothesis based on a sample of data, including null and alternative hypotheses.
