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Questions and Answers
What is the null hypothesis in the context of the research question regarding psychology students' average IQ?
What is the null hypothesis in the context of the research question regarding psychology students' average IQ?
- μ > 100
- μ ≠ 100
- μ < 100
- μ = 100 (correct)
Which significance level is commonly chosen in hypothesis testing?
Which significance level is commonly chosen in hypothesis testing?
- α = 0.20
- α = 0.01 (correct)
- α = 0.05 (correct)
- α = 0.10
What type of hypothesis test is appropriate for determining the average IQ of psychology students compared to the general population?
What type of hypothesis test is appropriate for determining the average IQ of psychology students compared to the general population?
- Paired t-test
- One-sample t-test (correct)
- One-sample z-test
- Two-sample t-test
If the calculated test statistic is less than or equal to the critical value, what is the decision?
If the calculated test statistic is less than or equal to the critical value, what is the decision?
What does effect size indicate in hypothesis testing?
What does effect size indicate in hypothesis testing?
In the context of hypothesis testing, which of the following best describes a Type I error?
In the context of hypothesis testing, which of the following best describes a Type I error?
What is the critical value for the one-sample t-test if the significance level is α = 0.05 and the test statistic is t = 3.45?
What is the critical value for the one-sample t-test if the significance level is α = 0.05 and the test statistic is t = 3.45?
Which statement about effect size is correct?
Which statement about effect size is correct?
What is the primary purpose of formulating a null hypothesis?
What is the primary purpose of formulating a null hypothesis?
In hypothesis testing, what does the alternative hypothesis represent?
In hypothesis testing, what does the alternative hypothesis represent?
Which of the following is NOT a step in the hypothesis testing process?
Which of the following is NOT a step in the hypothesis testing process?
What role does the p-value play in hypothesis testing?
What role does the p-value play in hypothesis testing?
What happens if the p-value is very small while testing a hypothesis?
What happens if the p-value is very small while testing a hypothesis?
Which of the following describes a Type I error in hypothesis testing?
Which of the following describes a Type I error in hypothesis testing?
In hypothesis testing, what does a significance level (alpha) typically define?
In hypothesis testing, what does a significance level (alpha) typically define?
Which statement about hypothesis testing is FALSE?
Which statement about hypothesis testing is FALSE?
What does the null hypothesis (H₀) state in a study comparing sample and population means?
What does the null hypothesis (H₀) state in a study comparing sample and population means?
Which statement best describes the alternative hypothesis (H₁ or Hₐ)?
Which statement best describes the alternative hypothesis (H₁ or Hₐ)?
When would a one-tailed test be appropriately used?
When would a one-tailed test be appropriately used?
What does a significance level (α) of 0.05 imply in hypothesis testing?
What does a significance level (α) of 0.05 imply in hypothesis testing?
What is the relationship between significance level (α) and Type I and Type II errors?
What is the relationship between significance level (α) and Type I and Type II errors?
What are critical values in hypothesis testing?
What are critical values in hypothesis testing?
In a two-tailed test with α = 0.05, what are the critical values in a z-distribution?
In a two-tailed test with α = 0.05, what are the critical values in a z-distribution?
Which condition leads to the acceptance of the null hypothesis?
Which condition leads to the acceptance of the null hypothesis?
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Study Notes
### Hypothesis Testing
- Hypothesis testing is a statistical method used to make inferences about populations based on sample data.
- The core principle is to assume a null hypothesis (no effect or difference) and use data to determine if this assumption is likely to be true.
- This method helps determine if observed patterns in sample data reflect true patterns in the larger population or are due to random chance.
- Key steps:
- Formulate a null hypothesis (H₀) and an alternative hypothesis (H₁).
- Collect data from a sample.
- Calculate a test statistic based on the data.
- Determine the probability of obtaining such a test statistic assuming the null hypothesis is true.
- Decide whether to reject or accept the null hypothesis based on this probability.
Alternative Hypothesis
- The alternative hypothesis (H₁) is the one the researcher seeks to support.
- It usually represents the opposite of the null hypothesis and suggests an effect or difference.
- Types of alternative hypotheses:
- Two-tailed (non-directional): States that there is a difference, but doesn't specify the direction (e.g., μ₁ ≠ μ₂).
- One-tailed (directional): Specifies the direction of the difference (e.g., μ₁ > μ₂ or μ₁ < μ₂).
- The choice between one-tailed and two-tailed tests depends on the research question and prior knowledge.
### Significance Level
- The significance level (α) represents the probability of rejecting the null hypothesis when it is actually true (Type I error).
- Common values for α are 0.05 and 0.01.
- Selecting α is a trade-off:
- A smaller α reduces the chance of Type I errors but increases the chance of Type II errors (failing to reject a false null hypothesis).
- A larger α does the opposite.
Critical Values
- Critical values are the boundaries of the rejection region in a distribution.
- If the test statistic falls outside these boundaries (beyond the critical values), the null hypothesis is rejected.
- Example: For a two-tailed test with α = 0.05 in a z-distribution, the critical values are ±1.96.
Decision Rules
- p-value < α: Reject the null hypothesis.
- p-value ≥ α: Fail to reject the null hypothesis.
### Effect Size
- Effect size is a measure of the strength of a phenomenon.
- It quantifies the difference between groups or the strength of a relationship between variables.
- Provides insight into the practical significance of a result beyond its statistical significance.
- Allows for comparison across studies, even with different sample sizes.
- Less affected by sample size than p-values.
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