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Questions and Answers
What is the primary focus of probability in contrast to statistics?
What is the primary focus of probability in contrast to statistics?
Which condition is necessary for a sample to be considered random?
Which condition is necessary for a sample to be considered random?
What does the percentile rank represent?
What does the percentile rank represent?
What is the null hypothesis primarily concerned with?
What is the null hypothesis primarily concerned with?
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What is the first step in hypothesis testing?
What is the first step in hypothesis testing?
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Which of the following best describes the goal of hypothesis testing?
Which of the following best describes the goal of hypothesis testing?
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In hypothesis testing, if the sample data shows a big discrepancy from the prediction, what should the conclusion be?
In hypothesis testing, if the sample data shows a big discrepancy from the prediction, what should the conclusion be?
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How is a percentile defined within a distribution?
How is a percentile defined within a distribution?
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What is the mean of a distribution of z-scores after transforming raw scores?
What is the mean of a distribution of z-scores after transforming raw scores?
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If the original distribution is negatively skewed, what will the distribution of z-scores look like?
If the original distribution is negatively skewed, what will the distribution of z-scores look like?
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What does the deviation score in the z-score formula measure?
What does the deviation score in the z-score formula measure?
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Which type of probability is based on observed data rather than theoretical assumptions?
Which type of probability is based on observed data rather than theoretical assumptions?
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For a sample with a mean ($ ext{μ}$) of 100 and a standard deviation ($ ext{σ}$) of 10, what z-score corresponds to a score of $X = 130$?
For a sample with a mean ($ ext{μ}$) of 100 and a standard deviation ($ ext{σ}$) of 10, what z-score corresponds to a score of $X = 130$?
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Which type of probability is defined based on personal judgment or estimation?
Which type of probability is defined based on personal judgment or estimation?
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In the z-score formula, what does the standard deviation ($ ext{σ}$) represent?
In the z-score formula, what does the standard deviation ($ ext{σ}$) represent?
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What X value corresponds to a z-score of $z = -1.50$ when the mean ($ ext{μ}$) is 60 and the standard deviation ($ ext{σ}$) is 8?
What X value corresponds to a z-score of $z = -1.50$ when the mean ($ ext{μ}$) is 60 and the standard deviation ($ ext{σ}$) is 8?
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What does the alternative hypothesis (H1) predict in an experiment?
What does the alternative hypothesis (H1) predict in an experiment?
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How is the credibility of the null hypothesis evaluated?
How is the credibility of the null hypothesis evaluated?
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What does a sample mean near the population mean signify in terms of the null hypothesis?
What does a sample mean near the population mean signify in terms of the null hypothesis?
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What role does the alpha level play in hypothesis testing?
What role does the alpha level play in hypothesis testing?
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If the alpha level is set to 0.05, what does this imply for the researcher?
If the alpha level is set to 0.05, what does this imply for the researcher?
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What does a confidence interval of approximately 95% correspond to in terms of the alpha level?
What does a confidence interval of approximately 95% correspond to in terms of the alpha level?
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What would indicate a Type I error in hypothesis testing?
What would indicate a Type I error in hypothesis testing?
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Which of the following would be a likely consequence of setting a very low alpha level (e.g., 0.01)?
Which of the following would be a likely consequence of setting a very low alpha level (e.g., 0.01)?
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What is the primary purpose of transforming raw scores into z-scores?
What is the primary purpose of transforming raw scores into z-scores?
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Why might two raw scores of 75 be incomparable?
Why might two raw scores of 75 be incomparable?
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What does a z-score indicate in relation to the mean?
What does a z-score indicate in relation to the mean?
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What is the average IQ score set at in most distributions?
What is the average IQ score set at in most distributions?
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What percentage of the population scores between 85 and 115 in a normal distribution?
What percentage of the population scores between 85 and 115 in a normal distribution?
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What is a common standard deviation for IQ tests?
What is a common standard deviation for IQ tests?
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Which statement accurately describes a raw score?
Which statement accurately describes a raw score?
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What percentage of the population typically scores above 130 on an IQ test?
What percentage of the population typically scores above 130 on an IQ test?
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What is the purpose of the critical region in hypothesis testing?
What is the purpose of the critical region in hypothesis testing?
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In statistical terms, what does a Type I error signify?
In statistical terms, what does a Type I error signify?
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How does a directional test differ from a non-directional test?
How does a directional test differ from a non-directional test?
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What does an alpha level of 0.05 imply in hypothesis testing?
What does an alpha level of 0.05 imply in hypothesis testing?
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What characterizes a left-tailed test?
What characterizes a left-tailed test?
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In the context of hypothesis testing, what outcome does a Type II error represent?
In the context of hypothesis testing, what outcome does a Type II error represent?
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Which statement is true regarding a two-tailed test compared to a directional test?
Which statement is true regarding a two-tailed test compared to a directional test?
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What does a higher alpha level generally indicate about the critical region?
What does a higher alpha level generally indicate about the critical region?
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What is a right-tailed test primarily used to assess?
What is a right-tailed test primarily used to assess?
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What is a critical characteristic of a two-tailed test?
What is a critical characteristic of a two-tailed test?
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When is it appropriate to use a one-tailed test?
When is it appropriate to use a one-tailed test?
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How is the alpha level distributed in a two-tailed test?
How is the alpha level distributed in a two-tailed test?
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What does effect size represent in research?
What does effect size represent in research?
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What does Cohen's d measure?
What does Cohen's d measure?
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What effect size value is interpreted as small according to Cohen's classification?
What effect size value is interpreted as small according to Cohen's classification?
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Which of the following best describes a one-tailed test in relation to power?
Which of the following best describes a one-tailed test in relation to power?
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Study Notes
Raw Score
- A raw score is the original, unprocessed score from a test or assessment.
- It represents an individual's performance without modifications.
- Raw scores are the starting point for statistical analysis.
- Raw scores lack context; a score of 75 on one test isn't directly comparable to a 75 on another if the tests vary in difficulty or scoring methods.
- Raw scores are often transformed into standardized scores (like z-scores) to allow for meaningful comparisons.
Z-score
- A z-score describes a score's position within a distribution.
- Raw scores, when transformed, provide more insightful information.
- Original measured scores are called raw scores.
- Transforming raw scores into z-scores helps to locate the exact position of scores within the distribution.
- Z-scores allow direct comparison with other standardized distributions.
- Z-scores have a mean of 0.
- The sign (+ or –) of a z-score indicates whether the score is above or below the mean.
- The absolute value of the z-score shows the distance from the mean in terms of standard deviations.
Mean and Standard Deviation
- The average IQ score is set at 100.
- Most individuals cluster around this mean.
- Standard deviation (SD) in IQ tests is usually 15 points.
- Approximately 68% of the population falls between 85 and 115 (one SD from the mean).
- About 95% of the population scores between 70 and 130 (two SD from the mean).
- Only about 2% score below 70 or above 130.
Z-score Formula
- The z-score formula is used to calculate a z-score from an x-value.
- It measures the distance between an x-value and the mean (also known as the deviation score).
- The deviation score is then divided by the standard deviation (σ) to represent the distance in terms of standard deviation units.
Z = (X - μ) / σ
(where X is the raw score, μ is the mean, and σ is the standard deviation)
Probability
- Probability is a fraction or proportion of possible outcomes.
- Several different types of probability exist:
- Classical Probability: Assumes equally likely outcomes.
- Empirical Probability: Based on observed data.
- Subjective Probability: Based on personal judgment.
- Axiomatic Probability: Based on fundamental principles.
Hypothesis Testing
- A hypothesis test uses sample data to evaluate a hypothesis about a population.
- A null hypothesis (H0) is stated, which assumes no effect or change.
- The alternative hypothesis (H1) assumes there is an effect or change.
- Sample data is used to determine whether or not to reject the null hypothesis.
- There are types of errors that can be made: a Type I and II error
Effect Size
- Effect size is a numerical measure of the strength of a relationship or difference between groups.
- A larger effect size indicates practical significance.
- Cohen's d is a common measure of effect size, calculated by the difference in means between groups, divided by the pooled standard deviations.
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Description
This quiz explores the concepts of raw scores and z-scores in statistics. It covers definitions, significance, and the transformation of raw scores into standardized scores for analysis. Understanding these concepts is crucial for accurate data interpretation.
