Stats Ch. 5 (exam three)

When raw scores are transformed to z-scores, their average deviation is what?

1

the standard deviation of any z-distribution is ________

1

With a sample mean of 50, and a standard deviation of 10: 1. What is z for X = 44? 2. What X produces z = -1.3

1. -.60 2. 37

All normal z-distributions share three important characteristics, they are:

1. A z-distribution always has the same shape as the raw score distribution - so if underlying raw score distrib. is normal, z-distrib. is normal too 2. the mean of any z-distribution is 0 - whatever mean of raw scores is, always transforms to 0 3. the standard deviation of any z-distribution is 1 - avg. deviation is now 1 for z-distrib.

a z-score always has 2 components, what are they?

1. a positive or negative sign indicating if the score is above or below the mean 2. the absolute value of the z-score (ignoring the sign) which indicates how FAR the score is from the mean in standard deviations

What three things does the central limit theorem communicate about sampling distributions?

1. a sampling distribution is always an approximately normal distribution 2. the mean of the sampling distribution equals the mean of the underlying raw score population used to create the sampling distribution 3. the standard deviation of the sampling distribution is mathematically related to the standard deviation of the raw score population

What three things do z-scores do?

1. they describe relative standing 2. they compare scores of different distributions 3. they compute the relative frequency of scores

What is the difference between a z-distribution and the sampling distribution of means?

A z distribution is a standardization of the distribution of a set of raw data. A sampling distribution of means is a hypothetical distribution (though it is technically a z -distribution) that we create by taking an infinite number of samples from a population and plotting the probability of getting that sample mean on the z distribution

Why are z-scores called standard scores?

Because z-scores use relative standing to equate scores from different variables or distributions so we have a standard way to compare them.

What are the steps for finding the relative frequency of sample means above or below a specified mean?

Compute the standard error of the mean, transform the sample mean into a z-score, and use the z-table to determine the proportion of the curve above or below the mean. This proportion is the expected relative frequency of the corresponding means.

How do we use a sampling distribution of means?

It is a model of all sample means to which we can compare our sample mean.

When using a sampling distribution of means, what do we mean by "underlying raw score population?"

It is the raw score population used to create a particular sampling distribution.

What is the standard error of the mean and what does it indicate?

It is the standard deviation of the sampling distribution of means, indicating the "average" deviation of sample means from the μ of the sampling distribution.

What is a sampling distribution of means?

It shows all possible sample means that occur when a particular raw score population is infinitely sampled using a particular

Kathy made a score of 75 on her biology exam. Shara made a score of 65 on her chemistry exam. Kathy insists that she did better than Shara (overall). A) Can Kathy make this assumption? B) Why or why not?

No, because you can't compare two separate distributions on equal terms. To interpret the meaning of these scores, we need a frame of reference to show how well Kathy and Shara did compared to other deviations in their classes. She must put these two scores on the same scale

What two factors determine the size of a z-score?

The size of the score's deviation and the size of the standard deviation.

A + z indicates the score is _______ the mean, a - z indicates the score is ________ the mean

above, below

negative z-scores become increasingly larger as we look to the _______ of the distribution, and these scores occur _______ frequently

become increasingly larger as we look to the left of the distribution, and these scores occur less frequently

Positive z-scores become increasingly larger as we look to the _______ of the distribution, and these scores occur ________ frequently

become increasingly larger as we look to the right of the distribution, and occur less frequently

How do we transform a raw score from a sample into a z-score?

by first subtracting the mean from the raw score and then dividing by the standard deviation

How do we transform an already known z-score to a raw score?

by multiplying the z-score times the standard deviation, and then adding the mean

a statistical principle that defines the mean, standard deviation, and shape of a sampling distribution

central limit theorem

the statistical principle called the _________ defines the shape, the mean, and the standard deviation of a sampling distribution

central limit theorem

the absolute value of the z indicates the scores __________ from the mean

distance

T or F: the mean of all z-distributions is equal to 1

false; the mean of all z-distributions is equal to ZERO

the standard normal curve is best used with what kind of data?

if 1. we have a large population or sample 2. the scores or interval or ratio 3. the scores are normally distributed

what is the importance of the central limit theorem?

it allows us to describe a sampling distribution without having to infinitely sample a population of raw scores

when computing a percentile, we add .50 to the proportion obtained from the z-table when the z-score has a _______ sign, but not when the z-score has a ______ sign

positive, negative

reflects the systematic evaluation of the score by comparing it to the sample or population in which the score occurs

relative standing

when we evaluate a raw score relative together scores in the data, we are describing the scores _______

relative standing

a frequency distribution showing all possible sample means that occur when samples of a particular size are drawn from a population

sampling distribution of means

A z-score indicates how far a score is from the mean when measured in what?

standard deviations

the standard deviation of the sampling distribution is called the ________

standard error of the mean

the standard deviation of the sampling distribution of means

standard error of the mean

To determine the relative frequency of raw scores, transform them into z-scores and then use the _____________

standard normal curve

a perfect normal curve that serves as a model of any approximately normal z-distribution

standard normal curve

z-scores are often referred to as what?

standard scores

If a score has a z-score of 0, what does this mean?

that the score is EQUAL TO the mean and is in the CENTER

what does a z-score indicate?

the distance a score is above or below the mean when measured in standard deviation units

Our first calculation when attempting to transform raw scores to z-scores is what?

the scores deviation, or how far a score is from the mean (X - sample mean)

we always refer to the population of raw scores used to create the sampling distribution as what?

the underlying raw score population

T or F: although scores may have different distributions, the location of each z-score is the same

true

T or F: you cannot compare two different distributions if they are not on the same scale

true

T or F: the z-distribution will always have the same shape as the raw score distribution

true; if the raw-score distribution shape is normal, the z-score distribution shape will be normal too

T or F: All z-distributions are laid out in the same way

true; this allows for z-scores to form a standard way to communicate relative standing

the mean of the sampling distribution always equals the mean of the _________ population

underlying raw score

the symbol for a z-score is

z

the distribution produced by transforming all raw scores in a distribution into z-scores

z-distribution

statistic that indicates the distance a score is fro its mean when measured in standard deviation units

z-score

to compare raw scores from two different variables, transform the scores into ________

z-scores

what are the 3 major uses of z-scores with individual's scores?

z-scores are used to determine 1. relative standing 2. compare scores from different variables 3. compute relative frequency and percentile

the mean of any z-distribution is _______

zero