Psychological Statistics Midterm Module 2
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Questions and Answers

What is the primary purpose of hypothesis testing?

  • To identify all variables without making predictions.
  • To establish a definitive conclusion about a population.
  • To evaluate a hypothesis using sample data. (correct)
  • To predict outcomes based on historical data.
  • Which step is NOT part of the four steps of a hypothesis test?

  • Make a decision
  • Collect data and compute results
  • Conduct a literature review (correct)
  • State the hypothesis
  • What does a Type I error indicate in hypothesis testing?

  • Rejecting a null hypothesis that is false.
  • Accepting a null hypothesis that is true.
  • Failing to reject a false null hypothesis.
  • Rejecting a null hypothesis that is true. (correct)
  • Which of the following best defines the alpha level in hypothesis testing?

    <p>The threshold for determining statistical significance.</p> Signup and view all the answers

    When calculating the z-score for a sample mean, which values are essential?

    <p>Sample size and population standard deviation.</p> Signup and view all the answers

    What is a Type II error in hypothesis testing?

    <p>Failing to detect an effect that is present.</p> Signup and view all the answers

    In hypothesis testing, what is meant by the critical region?

    <p>The extreme sample values that are very unlikely under the null hypothesis.</p> Signup and view all the answers

    What is primarily focused on in a hypothesis test?

    <p>The data collected</p> Signup and view all the answers

    Which factor can increase the power of a statistical test?

    <p>Increasing the sample size</p> Signup and view all the answers

    What must be determined to evaluate a hypothesis using sample data?

    <p>The relationship between two or more variables.</p> Signup and view all the answers

    What does a significant treatment effect not necessarily imply?

    <p>That the treatment effect is substantial</p> Signup and view all the answers

    What relationship does the alpha level have with the power of a test?

    <p>Increasing alpha increases power</p> Signup and view all the answers

    Which measure is used to estimate the real standard error when the value of σ is unknown?

    <p>Estimated Standard Error (sM)</p> Signup and view all the answers

    Which of the following statements is true regarding one-tailed and two-tailed tests?

    <p>One-tailed tests predict the direction of the treatment effect</p> Signup and view all the answers

    What does the degrees of freedom represent in a sample?

    <p>The number of scores that are independent and can vary</p> Signup and view all the answers

    What does measuring effect size provide insight into?

    <p>The strength or magnitude of a treatment effect</p> Signup and view all the answers

    What does a Type II error indicate in hypothesis testing?

    <p>A treatment effect is not detected when it does exist.</p> Signup and view all the answers

    Which factor is NOT considered when determining the boundaries of the critical region?

    <p>Sample size</p> Signup and view all the answers

    What happens to the standard deviation when a constant is added or subtracted from a dataset?

    <p>It is unaffected by the addition or subtraction of a constant.</p> Signup and view all the answers

    What is represented by the symbol β (beta) in hypothesis testing?

    <p>The probability of a Type II error</p> Signup and view all the answers

    What does a significant result in a statistical test imply about the null hypothesis?

    <p>It has been rejected.</p> Signup and view all the answers

    Which of the following is a characteristic of independent observations?

    <p>Each event outcome has no impact on the probability of the next.</p> Signup and view all the answers

    Which of the following best describes a one-tailed hypothesis test?

    <p>It specifies either an increase or a decrease in the population mean.</p> Signup and view all the answers

    What does a Type I error represent in hypothesis testing?

    <p>The null hypothesis is rejected when it is true.</p> Signup and view all the answers

    Which of the following assumptions is crucial for conducting hypothesis tests with z-scores?

    <p>The sample data must have a normal distribution.</p> Signup and view all the answers

    How does higher variability of scores influence a hypothesis test's outcome?

    <p>It decreases the z-score value.</p> Signup and view all the answers

    In hypothesis testing, what does it mean if sample data fall within the critical region?

    <p>The null hypothesis is rejected.</p> Signup and view all the answers

    What is the purpose of measuring effect size in hypothesis testing?

    <p>To measure the absolute magnitude of a treatment effect.</p> Signup and view all the answers

    Which factor would lead to a larger value for the z-score in hypothesis testing?

    <p>Increasing the number of scores in the sample.</p> Signup and view all the answers

    According to Cohen's criteria, how can effect size be standardized?

    <p>By measuring mean differences in terms of the standard deviation.</p> Signup and view all the answers

    In hypothesis testing, what does it mean if a result is said to be statistically significant?

    <p>The null hypothesis is unlikely to be true.</p> Signup and view all the answers

    What may cause a decrease in the chance of finding a significant treatment effect?

    <p>Lower sample size.</p> Signup and view all the answers

    What does the term 'effect size' refer to in the context of treatment variability?

    <p>A measurement that quantifies the impact of treatment on variability.</p> Signup and view all the answers

    What is the purpose of calculating a confidence interval?

    <p>To estimate the population parameter from a sample statistic.</p> Signup and view all the answers

    Which of the following correctly states the null hypothesis in a one-tailed t-test with the alternative hypothesis suggesting a decrease?

    <p>Ho: μ ≥ 0, H1: μ &lt; 0</p> Signup and view all the answers

    How is the critical value for a two-tailed test determined?

    <p>It utilizes the degrees of freedom and alpha level.</p> Signup and view all the answers

    In a t-test with 9 samples, what is the appropriate degree of freedom (df) to use?

    <p>8</p> Signup and view all the answers

    What is the critical value of t for a one-tailed test at α = 0.01 with 8 degrees of freedom?

    <p>2.896</p> Signup and view all the answers

    What does the term 'critical region' refer to in hypothesis testing?

    <p>The range of values in which we reject the null hypothesis.</p> Signup and view all the answers

    Which statement about hypothesis testing is false?

    <p>Rejecting the null hypothesis guarantees that it is false.</p> Signup and view all the answers

    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.
    • 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.

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