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Questions and Answers
In hypothesis testing, what is the initial assumption made about a hypothesis?
In hypothesis testing, what is the initial assumption made about a hypothesis?
- It is neither true nor false until tested.
- It is irrelevant to the testing process.
- It is false until proven true.
- It is true until proven otherwise. (correct)
Why is the null hypothesis often formulated as a statement of 'no difference'?
Why is the null hypothesis often formulated as a statement of 'no difference'?
- To simplify the mathematical calculations.
- To align with the alternative hypothesis.
- To provide a clear target for rejection. (correct)
- To ensure it is always accepted.
What does it mean to commit a Type I error in hypothesis testing?
What does it mean to commit a Type I error in hypothesis testing?
- Failing to reject a false alternative hypothesis.
- Rejecting a true null hypothesis. (correct)
- Rejecting a true alternative hypothesis.
- Accepting a false null hypothesis.
Under what circumstance is a Type II error committed?
Under what circumstance is a Type II error committed?
In a one-sided hypothesis test, what does the alternative hypothesis specify?
In a one-sided hypothesis test, what does the alternative hypothesis specify?
How does a two-sided test differ from a one-sided test in hypothesis testing?
How does a two-sided test differ from a one-sided test in hypothesis testing?
If $H_0 : \mu = 100$, which of the following alternative hypotheses ($H_a$) represents a two-sided test?
If $H_0 : \mu = 100$, which of the following alternative hypotheses ($H_a$) represents a two-sided test?
What does the level of significance, denoted by alpha ($\alpha$), represent in hypothesis testing?
What does the level of significance, denoted by alpha ($\alpha$), represent in hypothesis testing?
What does the critical region in hypothesis testing represent?
What does the critical region in hypothesis testing represent?
What is the first step in hypothesis testing?
What is the first step in hypothesis testing?
After stating the null and alternative hypotheses, what is the next step in hypothesis testing?
After stating the null and alternative hypotheses, what is the next step in hypothesis testing?
If a researcher sets $\alpha = 0.05$, what is the implication for the study's outcome?
If a researcher sets $\alpha = 0.05$, what is the implication for the study's outcome?
In a study comparing two population means ($\mu_1$ and $\mu_2$), the null hypothesis is $H_0 : \mu_1 = \mu_2$. Which alternative hypothesis ($H_a$) represents a two-sided test?
In a study comparing two population means ($\mu_1$ and $\mu_2$), the null hypothesis is $H_0 : \mu_1 = \mu_2$. Which alternative hypothesis ($H_a$) represents a two-sided test?
What is the purpose of computing the test statistic in hypothesis testing?
What is the purpose of computing the test statistic in hypothesis testing?
Which of the following outcomes would lead to the rejection of the null hypothesis?
Which of the following outcomes would lead to the rejection of the null hypothesis?
Flashcards
Hypothesis
Hypothesis
A tentative theory that may or may not be true, but is initially assumed to be true until new evidence suggests otherwise.
Null Hypothesis
Null Hypothesis
The hypothesis of 'no difference,' formulated to be rejected.
Alternative Hypothesis
Alternative Hypothesis
A hypothesis that contradicts the null hypothesis. It is supported if the null hypothesis is rejected.
Type I Error
Type I Error
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Type II Error
Type II Error
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One-Sided Test
One-Sided Test
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Two-Sided Test
Two-Sided Test
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Level of Significance (alpha)
Level of Significance (alpha)
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Critical Region
Critical Region
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Basic Steps in Hypothesis Testing
Basic Steps in Hypothesis Testing
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Study Notes
- A hypothesis is a statement or tentative theory, that may or may not be true.
- A hypothesis is assumed true until new evidence suggests otherwise.
- Hypotheses can be proposed from preliminary observations, guesses, or previous experiences.
Types of Hypothesis
- The null hypothesis, denoted by Ho, states there is "no difference."
- The null hypothesis is formulated for the purpose of being rejected.
- The alternative hypothesis, denoted by Ha or H1, contradicts the null hypothesis.
- If the null hypothesis is rejected, the alternative hypothesis is supported.
- The alternative hypothesis is the operational statement of the experimenter's research hypothesis.
Types of Errors
- A Type I error occurs when the null hypothesis is rejected when it is actually true.
- A Type II error occurs when the null hypothesis is accepted when it is false.
- If Ho is true and is accepted, there is a correct decision.
- If Ho is false and is rejected, there is a correct decision.
Types of Tests
- In a one-sided test, the alternative hypothesis specifies that the unknown population parameter is entirely above or entirely below the specified value of Ho.
- A one-sided test is also called a one-tailed or directional test.
- In a two-sided test, the alternative hypothesis specifies that the unknown population parameter can lie on either side of the value specified by Ho.
- A two-sided test is also called a two-tailed or non-directional test.
Examples
- One sided test
- Ho : μ = 100, Ha : μ < 100
- Ho : μ = 100, Ha : μ > 100
- Two-sided test
- Ho : μ = 100, Ha : μ ≠ 100
- Ho : μ₁ = μ₂, Ha : μ₁ - μ₂ ≠ 0
Level of Significance
- The probability of committing a Type I error is denoted by alpha (α).
- The probability of committing a Type II error is denoted by beta (β) = 1 - α.
Critical Region
- Critical region refers to the set of all values of the test statistics that would cause the null hypothesis to be rejected.
Basic Steps in Hypothesis Testing
- State the null hypothesis (Но) and the alternative hypothesis (Ha).
- Specify the level of significance α and the sample size n.
- Determine the test statistic.
- Define the critical region or decision rule.
- Compute the test statistics for a sample size n.
- Make a decision/conclusion.
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