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Questions and Answers
What is the primary purpose of hypothesis testing?
What is the primary purpose of hypothesis testing?
Which step is NOT part of the four steps of a hypothesis test?
Which step is NOT part of the four steps of a hypothesis test?
What does a Type I error indicate in hypothesis testing?
What does a Type I error indicate in hypothesis testing?
Which of the following best defines the alpha level in hypothesis testing?
Which of the following best defines the alpha level in hypothesis testing?
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When calculating the z-score for a sample mean, which values are essential?
When calculating the z-score for a sample mean, which values are essential?
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What is a Type II error in hypothesis testing?
What is a Type II error in hypothesis testing?
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In hypothesis testing, what is meant by the critical region?
In hypothesis testing, what is meant by the critical region?
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What is primarily focused on in a hypothesis test?
What is primarily focused on in a hypothesis test?
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Which factor can increase the power of a statistical test?
Which factor can increase the power of a statistical test?
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What must be determined to evaluate a hypothesis using sample data?
What must be determined to evaluate a hypothesis using sample data?
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What does a significant treatment effect not necessarily imply?
What does a significant treatment effect not necessarily imply?
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What relationship does the alpha level have with the power of a test?
What relationship does the alpha level have with the power of a test?
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Which measure is used to estimate the real standard error when the value of σ is unknown?
Which measure is used to estimate the real standard error when the value of σ is unknown?
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Which of the following statements is true regarding one-tailed and two-tailed tests?
Which of the following statements is true regarding one-tailed and two-tailed tests?
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What does the degrees of freedom represent in a sample?
What does the degrees of freedom represent in a sample?
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What does measuring effect size provide insight into?
What does measuring effect size provide insight into?
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What does a Type II error indicate in hypothesis testing?
What does a Type II error indicate in hypothesis testing?
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Which factor is NOT considered when determining the boundaries of the critical region?
Which factor is NOT considered when determining the boundaries of the critical region?
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What happens to the standard deviation when a constant is added or subtracted from a dataset?
What happens to the standard deviation when a constant is added or subtracted from a dataset?
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What is represented by the symbol β (beta) in hypothesis testing?
What is represented by the symbol β (beta) in hypothesis testing?
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What does a significant result in a statistical test imply about the null hypothesis?
What does a significant result in a statistical test imply about the null hypothesis?
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Which of the following is a characteristic of independent observations?
Which of the following is a characteristic of independent observations?
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Which of the following best describes a one-tailed hypothesis test?
Which of the following best describes a one-tailed hypothesis test?
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What does a Type I error represent in hypothesis testing?
What does a Type I error represent in hypothesis testing?
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Which of the following assumptions is crucial for conducting hypothesis tests with z-scores?
Which of the following assumptions is crucial for conducting hypothesis tests with z-scores?
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How does higher variability of scores influence a hypothesis test's outcome?
How does higher variability of scores influence a hypothesis test's outcome?
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In hypothesis testing, what does it mean if sample data fall within the critical region?
In hypothesis testing, what does it mean if sample data fall within the critical region?
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What is the purpose of measuring effect size in hypothesis testing?
What is the purpose of measuring effect size in hypothesis testing?
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Which factor would lead to a larger value for the z-score in hypothesis testing?
Which factor would lead to a larger value for the z-score in hypothesis testing?
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According to Cohen's criteria, how can effect size be standardized?
According to Cohen's criteria, how can effect size be standardized?
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In hypothesis testing, what does it mean if a result is said to be statistically significant?
In hypothesis testing, what does it mean if a result is said to be statistically significant?
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What may cause a decrease in the chance of finding a significant treatment effect?
What may cause a decrease in the chance of finding a significant treatment effect?
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What does the term 'effect size' refer to in the context of treatment variability?
What does the term 'effect size' refer to in the context of treatment variability?
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What is the purpose of calculating a confidence interval?
What is the purpose of calculating a confidence interval?
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Which of the following correctly states the null hypothesis in a one-tailed t-test with the alternative hypothesis suggesting a decrease?
Which of the following correctly states the null hypothesis in a one-tailed t-test with the alternative hypothesis suggesting a decrease?
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How is the critical value for a two-tailed test determined?
How is the critical value for a two-tailed test determined?
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In a t-test with 9 samples, what is the appropriate degree of freedom (df) to use?
In a t-test with 9 samples, what is the appropriate degree of freedom (df) to use?
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What is the critical value of t for a one-tailed test at α = 0.01 with 8 degrees of freedom?
What is the critical value of t for a one-tailed test at α = 0.01 with 8 degrees of freedom?
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What does the term 'critical region' refer to in hypothesis testing?
What does the term 'critical region' refer to in hypothesis testing?
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Which statement about hypothesis testing is false?
Which statement about hypothesis testing is false?
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Study Notes
Statistical Inference and Hypothesis Testing
- Every sample mean (M) has a z-score indicating its position within the distribution of sample means.
- Hypothesis: Predicts the relationship between variables; serves as a scientific guess.
- A hypothesis test evaluates a hypothesis about a population using sample data.
- Hypothesis testing employs statistical analysis to address research questions.
Steps in Hypothesis Testing
- Step 1: State the hypothesis.
- Step 2: Set criteria for making decisions based on data.
- Step 3: Collect data and compute sample statistics.
- Step 4: Make a decision regarding the null hypothesis.
Types of Errors in Hypothesis Testing
- Type I Error (False Positive): Rejecting a true null hypothesis, indicating treatment effect where none exists.
- Type II Error (False Negative): Failing to reject a false null hypothesis, missing a real treatment effect.
- Critical region determined by alpha level, which defines extreme sample values unlikely if the null hypothesis is true.
Z-Scores
- Z-score for Population: Reflects an individual score's position in the entire score distribution.
- Z-score for Sample: Reflects a sample mean's position within the distribution of sample means.
Assumptions for z-Score Hypothesis Tests
- Random Sampling: Ensures sample is representative of the population.
- Independent Observations: The occurrence of one event does not affect another.
- Value of σ remains unchanged by treatment, affecting only the mean, not standard deviation.
Reporting Results in Statistical Tests
- A significant result indicates the null hypothesis is rejected, unlikely to occur by chance alone.
- Directional (One-Tailed) Hypothesis Tests specify expected direction of effect (increase/decrease).
Measuring Effect Size
- Effect size quantifies the magnitude of a treatment effect, independent of sample size.
- Cohen (1988) suggested standardizing effect size by measuring mean difference relative to standard deviation.
Factors Influencing Hypothesis Test Outcomes
- Score Variability: Higher variability may decrease likelihood of significant results due to reduced z-score value.
- Sample Size: Larger samples provide smaller standard errors and larger z-scores, increasing power.
- Alpha Level: Lowering alpha level reduces test power but decreases Type I error risk.
Power of a Statistical Test
- Probability of correctly rejecting a false null hypothesis increases with larger sample sizes.
- Parametric tests generally have greater power than non-parametric counterparts.
- Power calculations help determine if the sample size is sufficient.
t-Statistic in Hypothesis Testing
- Used when population parameters are unknown, forms the basis of t-tests.
- Critical region locations depend on the degrees of freedom (df) determined by sample size.
Confidence Intervals
- Represent a range of values around a sample statistic, predicting the population parameter.
- Confidence intervals provide insight into where the true population parameter likely falls.
T-Test for Related Samples
- Hypotheses must clearly define expected differences between conditions (e.g., swearing and pain tolerance).
- Specify the alpha level to determine critical values for decision-making in hypothesis testing.
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Description
This quiz covers key concepts from Module 2 of Psychological Statistics, focusing on hypothesis testing, effect size, and types of errors. It explores the relationship between sample means and z-scores, providing a comprehensive assessment of your understanding of statistical inference.
