Chapter 5 - Review Questions Flashcards
What are the three major uses of z-scores with individuals’ scores?
z-scores are used to determine relative standing, compare scores from different variables, and compute relative frequency and percentile.
What does a z-score indicate?
A z-score indicates the distance a score is above or below the mean when measured in standard deviation units.
What two factors determine the size of a z-score?
What is a z-distribution?
It is the distribution that results from transforming a distribution of raw scores into z-scores.
Is a z-distribution always a normal distribution?
No, only when the raw scores are normally distributed.
What is the mean and standard deviation of any z-distribution?
The mean is 0 and the standard deviation is 1.
Why are z-scores called “standard scores”?
It is our model of the perfect normal z-distribution.
How is it used to describe raw scores?
It is used as a model of any normal distribution of raw scores after being transformed to z-scores.
The standard normal curve is most appropriate when raw scores have what characteristics?
When scores are a large group of normally distributed interval or ratio scores.
An instructor says that your test grade produced a very large positive z-score. (a)
How well did you do on the test? (b) What do you know about your raw score’s
relative frequency? (c) What does it mean if you scored at the 80th percentile? (d)
What distribution would the instructor examine to make the conclusion in part c?
What are the steps for using the z-table to find: the relative frequency of raw scores in a specified slice of a distribution?
Convert the raw score that marks the slice to z ; find in column B or C the proportion in the slice, which is also the relative frequency of the scores in the slice.
What are the steps for using the z-table to find: the relative frequency of raw scores in a specified slice of a distribution?
Convert the raw score to z; the proportion of the curve to the left of z (in column C) becomes the percentile.
What are the steps for using the z-table to find: the percentile for a raw score above the mean?
Convert the raw score to z ; the proportion of the curve between the z and the mean (in column B) plus .50 becomes the percentile.
What are the steps for using the z-table to find: the raw score that cuts off a specified relative frequency or percentile?
Find the specified proportion in column B or C, identify the z in column A, and transform the z to its corresponding raw score.
(a) What is a sampling distribution of means? (b) How do we use it? (c) What do we
mean by the “underlying raw score population”?
What three things does the central limit theorem tell us about the sampling distribution of means?
That it is normally distributed, that its μ equals the μ of the underlying raw score population, and that its standard deviation is related to the standard deviation of the raw score population.
Why is the central limit theorem useful when we want to describe a sample mean?
Because it describes the sampling distribution for any population without our having to actually measure all possible sample means.
What is the standard error of the mean and what does it indicate?
What are the steps for finding the relative frequency of sample means above or below a specified mean?
