Worksheets4 Stats - Normal Distribution and Z-Scores
Total questions: 24
Worksheet time: 12mins
What are the two reasons for studying distributions of scores in psychology?
To classify data as either parametric or non-parametric.
To explain the distribution of scores and compare distributions across groups.
To identify outliers and compare variance.
To determine standard deviations and medians.
What is the most common type of distribution seen in nature?
Skewed distribution.
Bimodal distribution.
Normal distribution.
Poisson distribution.
What property of the normal distribution allows calculation of probabilities?
Knowing the mean and standard deviation enables calculation of cumulative probabilities.
Its symmetry.
Its bell shape.
The height of its peak.
What is a key assumption of most inferential statistical tests?
That data are positively skewed.
That the data are normally distributed.
That the median equals the mode.
That the distribution has no outliers.
Why might normally distributed data not always be realistic?
Sampling procedures are rarely perfect.
The standard deviation is usually too large.
Outliers tend to dominate distributions.
Most variables are bimodal.
What does the Central Limit Theorem state about sampling distributions of means?
They contain no variability.
They approximate a normal curve regardless of the underlying variable distribution.
They follow a bimodal curve if the population data are skewed.
They have a mean larger than the population mean.
What is a sampling distribution?
A frequency distribution of standardized scores.
A distribution of means from multiple random samples of the same population.
A curve that compares medians across samples.
A dataset containing raw scores from a sample.
What is a key feature of a normal distribution curve?
It is skewed to the right.
It has no variability.
It is symmetrical and bell-shaped.
It contains equal proportions of z-scores and raw scores.
What is a z-score?
A ratio of mean to median.
A value that identifies an outlier.
A standardized score expressed in terms of standard deviation units.
A raw score in a normal distribution.
Why are z-scores useful?
They calculate probabilities of medians.
They identify whether a dataset is skewed or kurtotic.
They provide the raw score's rank within a dataset.
They allow comparison of scores on different scales and locate an individual’s position within a distribution.
How is a z-score calculated?
By multiplying the standard deviation by the mean.
By subtracting the mean from the score and dividing by the standard deviation.
By finding the difference between the highest and lowest scores.
By adding the raw score and the standard deviation.
What does a z-score of 0 represent?
A score two standard deviations above the mean.
A value at the 50th percentile.
A raw score of 0.
A score equal to the mean.
What does a positive z-score indicate?
A score above the mean.
A score below the mean.
A score with no variability.
A score equal to the mode.
What does a negative z-score indicate?
A score equal to the mean.
A score below the mean.
A score at the 95th percentile.
A score that cannot be standardized.
How far are most scores (68%) from the mean in a normal distribution?
Within ±1 standard deviation.
Within ±0.5 standard deviations.
Within ±2 standard deviations.
Within ±3 standard deviations.
How far are 95% of scores from the mean in a normal distribution?
Within ±1 standard deviation.
Within ±2 standard deviations.
Within ±3 standard deviations.
Within ±4 standard deviations.
How far are 99.7% of scores from the mean in a normal distribution?
Within ±3 standard deviations.
Within ±1 standard deviation.
Within ±2 standard deviations.
Within ±4 standard deviations.
How can a raw score be derived from a z-score?
Subtract the mean from the z-score and divide by the standard deviation.
Multiply the z-score by the standard deviation and add the mean.
Multiply the z-score by the mean and subtract the standard deviation.
Add the raw score to the standard deviation.
Why is standardization important when comparing scores?
It ensures all variables have equal variability.
It adjusts for differences in sample size.
Different scales have different means, standard deviations, and ranges.
It removes outliers from a dataset.
What does the numerical value of a z-score represent?
The distance of a score from the mean in standard deviation units.
The degree of skewness in the dataset.
The difference between the raw score and the median.
The percentile rank of the score in a normal distribution.
What does the Central Limit Theorem imply for population inference?
The population mean becomes less relevant as samples are drawn.
The sampling distribution will always be positively skewed.
The sample mean approximates the population mean as sample size increases.
The range of the sample mean decreases over time.
What is the relationship between a normal distribution and probabilities?
The normal curve provides the mode for any dataset.
The normal curve allows calculation of the probability of scores occurring within specific ranges.
The normal curve shows the range of variability across datasets.
The normal curve always predicts a z-score of 0 for the mean.
How does the normal distribution relate to neuroticism levels in the population?
Neuroticism levels in small samples tend to have leptokurtic distributions.
Neuroticism levels cannot be assessed using a normal distribution.
Neuroticism levels follow a Poisson curve in all populations.
Neuroticism levels are an example of a variable often distributed normally in large samples.
What is the main limitation of using a single raw score across different tests?
The score assumes all tests are normally distributed.
The score lacks comparability due to differing metrics like means and standard deviations.
The score eliminates variability from the dataset.
The score fails to account for skewness or kurtosis.
