Questions and Answers
What type of analysis should Mike use to compare the GPA between freshmen, sophomores, juniors, and seniors?
one-way ANOVA
What type of analysis should Mike use after regrouping his participants into upperclassmen and lowerclassmen?
t-test
Moa's experiment on employee productivity is a ___ design.
between participant, quasi-experimental design
What is the median and mode of your last test with an average of 70 and a normal distribution?
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What was your grade if your z-score was +2 with an average of 70 and standard deviation of 10?
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What percentage of your class scored between 60 and 80 if the standard deviation is 10 and the average is 70?
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What is your friend's z-score if they scored 55 with an average of 50 and a standard deviation of 10?
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What score does a z of 0 correspond to if the average is 50?
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95% of the people get between ___ and ___ dates based on an average of 5 with a standard deviation of 1.
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What happens to the interval when changing from a 95% confidence interval to a 99% confidence interval?
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What happens to the 95% confidence interval when increasing the sample size from n=50 to n=5000?
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According to the Central Limit Theorem, what happens to the mean of the sample as the sample size increases?
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What happens to the variability of the distribution of sample means if the sample size increases?
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According to the Central Limit Theorem, what happens to the shape of the sample as the sample size increases?
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What can be expected about the shape of the sampling distribution of sample means if the sample size goes from 5 to 10,000?
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How are the variance and the standard deviation different?
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How are the variance and the standard deviation related?
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If you scored an IQ of 130, what would your z-score be if the mean is 100 and standard deviation is 15?
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What z-score best corresponds to a test score at the 50th percentile?
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Which analysis should your professor use to predict your GPA based on the number of classes you take?
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What analysis is used in a study comparing the tip percentage between two groups?
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68% of all pizza delivery times range between ___ and ___.
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If you scored an IQ of 122.5, what would your z-score be?
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What does the graph show regarding the central limit theorem?
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What is a z-score?
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Study Notes
Analysis Types
- One-way ANOVA is used to compare the GPA across multiple groups, such as freshmen, sophomores, juniors, and seniors.
- A t-test is appropriate for comparing the GPA between two groups, like upperclassmen and lowerclassmen.
Experimental Design
- A between-participant, quasi-experimental design measures productivity differences between employees working different schedules (10 hour days vs. 8 hour days).
Statistical Data
- In a normally distributed test scoring, both the median and mode are equal to the average score, which is 70.
- A z-score of +2 corresponds to a grade of 90 when the test mean is 70 and the standard deviation is 10.
Percentile and Standard Deviation
- Approximately 68.26% of scores fall within one standard deviation (60-80) from the mean in a normal distribution.
- A z-score calculates the position of a score in relation to the mean, with a +0.5 indicating a score of 55 in a test with a mean of 50.
Confidence Intervals
- Changing a confidence interval from 95% to 99% results in a wider range due to increased uncertainty.
- Increasing sample size from n=50 to n=5000 narrows the confidence interval, improving precision.
Central Limit Theorem
- With an increased sample size, the sample mean tends closer to the population mean, and the variability of sample means decreases.
- As sample size grows, the distribution of sample means approaches a normal shape, even if the parent population is skewed.
Variance and Standard Deviation
- Variance represents the average of squared deviations from the mean and is typically larger than standard deviation.
- Standard deviation is the square root of the variance.
IQ Scores and Percentiles
- An IQ of 130 corresponds to a z-score of 2, while an IQ of 122.5 corresponds to a z-score of 1.5.
- Scoring at the 50th percentile corresponds to a z-score of 0, indicating an average performance.
Predictive Analysis
- Regression analysis is used to predict outcomes, such as GPA based on the number of classes taken.
Testing and Percentages
- A study comparing tip percentages between groups receiving chocolate versus those who don't is analyzed with a t-test.
- In a pizza delivery time distribution with a mean of 30 minutes and standard deviation of 5 minutes, 68% of delivery times fall between 25 and 35 minutes.
Z-score Definition
- A z-score measures how many standard deviations a score deviates from the mean, providing context for an individual score within a distribution.
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Description
Test your knowledge on various statistical analysis types, including ANOVA, t-tests, and z-scores. This quiz covers experimental design and key concepts such as confidence intervals and standard deviations. Ideal for students looking to solidify their understanding of statistics.