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The distribution of z-scores will always have a mean of one.
The distribution of z-scores will always have a mean of one.
False
Transforming raw scores into z-scores can change the shape of the distribution.
Transforming raw scores into z-scores can change the shape of the distribution.
False
A z-score of -1.50 indicates the value is below the mean.
A z-score of -1.50 indicates the value is below the mean.
True
Classical probability is based on the assumption of equally likely outcomes.
Classical probability is based on the assumption of equally likely outcomes.
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If a distribution has a mean of 100 and a standard deviation of 10, a score of X = 130 will correspond to a z-score of 3.
If a distribution has a mean of 100 and a standard deviation of 10, a score of X = 130 will correspond to a z-score of 3.
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Empirical probability is derived from theoretical assumptions.
Empirical probability is derived from theoretical assumptions.
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A deviation score measures the distance in points between X and μ.
A deviation score measures the distance in points between X and μ.
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Subjective probability relies on exact calculations rather than personal judgment.
Subjective probability relies on exact calculations rather than personal judgment.
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The null hypothesis is identified by the symbol H1.
The null hypothesis is identified by the symbol H1.
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In hypothesis testing, conclusions are drawn based on the sample mean and its relation to the predicted characteristics.
In hypothesis testing, conclusions are drawn based on the sample mean and its relation to the predicted characteristics.
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Probability only relates to analyzing data collected from past events.
Probability only relates to analyzing data collected from past events.
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Random sampling requires that every individual in the population has an equal chance of being selected.
Random sampling requires that every individual in the population has an equal chance of being selected.
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Percentiles measure the relative standing of a score by identifying its rank within a distribution.
Percentiles measure the relative standing of a score by identifying its rank within a distribution.
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Sampling without replacement must be used to ensure constant probabilities when selecting more than one individual.
Sampling without replacement must be used to ensure constant probabilities when selecting more than one individual.
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A hypothesis test begins by selecting a sample from the population before stating any hypotheses.
A hypothesis test begins by selecting a sample from the population before stating any hypotheses.
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A raw score reflects an individual's performance without any modifications or transformations.
A raw score reflects an individual's performance without any modifications or transformations.
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Z-scores are used to mask the actual value of a raw score rather than to provide context.
Z-scores are used to mask the actual value of a raw score rather than to provide context.
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A raw score of 75 on one test is always directly comparable to a raw score of 75 on another test.
A raw score of 75 on one test is always directly comparable to a raw score of 75 on another test.
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The average IQ score is typically set at 100.
The average IQ score is typically set at 100.
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Approximately 68% of the population scores between 70 and 130 in IQ testing.
Approximately 68% of the population scores between 70 and 130 in IQ testing.
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Z-scores allow for comparisons between different distributions by standardizing the scores.
Z-scores allow for comparisons between different distributions by standardizing the scores.
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Only about 2% of the population scores below 85 in IQ testing.
Only about 2% of the population scores below 85 in IQ testing.
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In IQ testing, a standard deviation is typically 10 points.
In IQ testing, a standard deviation is typically 10 points.
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The critical region is the set of values for the test statistic that would lead to accepting the null hypothesis.
The critical region is the set of values for the test statistic that would lead to accepting the null hypothesis.
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A right-tailed test assesses whether a parameter is less than a specified value.
A right-tailed test assesses whether a parameter is less than a specified value.
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A Type I error occurs when a researcher accepts a null hypothesis that is actually false.
A Type I error occurs when a researcher accepts a null hypothesis that is actually false.
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A two-tailed test is used to detect significant differences in either direction.
A two-tailed test is used to detect significant differences in either direction.
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A one-tailed test can assess if a parameter is greater than or less than a designated value.
A one-tailed test can assess if a parameter is greater than or less than a designated value.
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Direction tests are often called two-tailed tests because they analyze both sides of the distribution.
Direction tests are often called two-tailed tests because they analyze both sides of the distribution.
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In a one-tailed test, the alpha level is allocated to both tails of the distribution.
In a one-tailed test, the alpha level is allocated to both tails of the distribution.
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Effect size indicates the strength of the relationship between two variables.
Effect size indicates the strength of the relationship between two variables.
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The null hypothesis predicts that there is a change, a difference, or a relationship in the general population.
The null hypothesis predicts that there is a change, a difference, or a relationship in the general population.
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Setting an alpha level of 0.05 means that 95% of the distribution will be in the critical region.
Setting an alpha level of 0.05 means that 95% of the distribution will be in the critical region.
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Cohen's d values are interpreted as small (0.5), medium (0.2), or large (0.8) effects.
Cohen's d values are interpreted as small (0.5), medium (0.2), or large (0.8) effects.
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In a left-tailed test, the critical region for rejecting the null hypothesis is located entirely in the positive direction.
In a left-tailed test, the critical region for rejecting the null hypothesis is located entirely in the positive direction.
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An alpha level of 0.01 corresponds to a 1% risk of making a Type II error.
An alpha level of 0.01 corresponds to a 1% risk of making a Type II error.
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In a two-tailed test, each critical region receives half of the alpha level.
In a two-tailed test, each critical region receives half of the alpha level.
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A Type II error occurs when the null hypothesis is rejected when it is actually false.
A Type II error occurs when the null hypothesis is rejected when it is actually false.
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A sample mean close to 15.8 supports the null hypothesis regarding red shirts.
A sample mean close to 15.8 supports the null hypothesis regarding red shirts.
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The significance level is typically set to values higher than 0.10 in most research contexts.
The significance level is typically set to values higher than 0.10 in most research contexts.
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A large effect size indicates that a research finding has limited practical significance.
A large effect size indicates that a research finding has limited practical significance.
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The phrase 'As sleep deprivation increases, cognitive performance decreases' is an example of a directional hypothesis.
The phrase 'As sleep deprivation increases, cognitive performance decreases' is an example of a directional hypothesis.
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A one-tailed test is appropriate when there is no strong prior evidence suggesting a direction.
A one-tailed test is appropriate when there is no strong prior evidence suggesting a direction.
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If the null hypothesis is correctly rejected, this means it was actually true.
If the null hypothesis is correctly rejected, this means it was actually true.
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A confidence interval of approximately 95% corresponds to an alpha level of 0.05.
A confidence interval of approximately 95% corresponds to an alpha level of 0.05.
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The independent variable has no effect on the dependent variable under the alternative hypothesis.
The independent variable has no effect on the dependent variable under the alternative hypothesis.
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Type I errors occur when the null hypothesis is incorrectly accepted.
Type I errors occur when the null hypothesis is incorrectly accepted.
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Study Notes
Raw Score
- A raw score is the original, unprocessed score from a test or assessment.
- It reflects the individual's performance without any modifications.
- Raw scores provide numerical values but lack context in isolation.
- Raw scores from different tests can't be directly compared if they differ in difficulty or scoring methods.
Z-score
- A z-score is a standardized score that provides information about a score's position within a distribution.
- Z-scores transform raw scores into new values conveying more information.
- Z-scores indicate the exact location of the original score within the distribution.
- Z-scores allow for direct comparison across different distributions.
Mean Score
- The average IQ score is set at 100, representing the peak of the bell curve.
- Most individuals' scores cluster around this mean.
- Standard deviation in IQ testing is typically 15 points.
- Approximately 68% of the population scores between 85 and 115 (within one standard deviation of the mean).
- About 95% score between 70 and 130 (within two standard deviations of the mean).
Z-score Formula
- The z-score formula calculates the deviation score between X and μ, divided by σ.
- It indicates whether a score is above or below the mean.
- The distance is measured in terms of standard deviation units.
Sample Z-score Calculation
- For a distribution with mean μ = 100 and standard deviation σ = 10, a score of X = 130 corresponds to a z-score of 3.00.
- For a distribution with mean μ = 60 and standard deviation σ = 8, a z-score of -1.50 corresponds to an X value of 48.
Probability
- Probability, for a situation with several possible outcomes, is a fraction or proportion of all possible outcomes for any specific outcome.
- Types of probability include classical, empirical, and subjective.
Hypothesis Testing
- Hypothesis testing is a statistical method to evaluate a hypothesis about a population.
- First, state a hypothesis about a population concerning a population parameter.
- Obtain a random sample from the population.
- Compare the sample data with the hypothesis's prediction.
- If the sample data aligns with the prediction, the hypothesis is considered reasonable.
Alpha Level
- The alpha level (significance level) is the probability of making a Type I error (rejecting a true null hypothesis).
- It's often set at 0.05 (5%).
- The critical region consists of values for the test statistic that lead to rejecting the null hypothesis (when sufficiently extreme).
Type I and Type II Errors
- A Type I error occurs when a true null hypothesis is rejected.
- A Type II error occurs when a false null hypothesis is not rejected.
Directional Tests
- One-tailed tests (directional tests) evaluate if a parameter is greater or less than a certain value.
- Two-tailed tests evaluate if a parameter is significantly different from a certain value without specifying a direction.
Effect Size
- Effect size is a numerical value expressing the strength of a relationship between two variables.
- Cohen’s d measures the standardized difference between two means (sample means), providing a measure of effect size in terms of deviations from the mean.
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Description
This quiz covers the fundamental concepts of raw scores, z-scores, and mean scores, particularly in the context of assessments and IQ testing. It explains their definitions, significance, and how they relate to one another. Test your understanding and application of these scoring methods.
