Chapter 6: Part 2

Question 1

How can the knowledge of the determination of a z-score be determined?

Answer 1

Probabilities associated with individual sample means can be found, laying the basis for testing hypotheses about sample means

Question 2

When can the normal distribution be used in place of the binomial distribution?

Answer 2

When there are large numbers of observations

Question 3

What is a sampling distribution?

Answer 3

Frequency distribution of the complete set of a statistic derived from random samples of a given size drawn from a population

Question 4

What is a standard normal distribution?

Answer 4

The mean is 0 and the sd is 1

Question 5

What is the standard normal distribution used to represent?

Answer 5

Real-valued random variable whose distributions are not known

Question 6

Why is the standard normal distribution useful?

Answer 6

Because any normal distribution can be turned into a standard normal distribution

Question 7

What does a complete set of values for the sample mean allow us to determine?

Answer 7

probability of particular sample means

Question 8

What is the symbol for the mean of the distribution of sample means?

Answer 8

Ux(x has a bar)

Question 9

What is the symbol for the standard deviation of the mean?

Answer 9

o x with a bar

Question 10

What is the standard error of the mean?

Answer 10

Standard deviation of the sample means

Question 11

How can you calculate standard error?

Answer 11

the standard deviation (σ) divided by the square root of the sample size (n). It’s written as: SEM = σ/√n

Question 12

When do you use the standard deviation formula?

Answer 12

When you want to understand the spread of data points in a single sample

Question 13

When do you use the standard error formula?

Answer 13

Dealing with multiple samples from a population and you want to understand how much the sample means vary

Question 14

When do you use standard error vs. standard deviation?

Answer 14

standard deviation is used when analyzing individual data points, while standard error is used when analyzing sample means.

Question 15

What happens when the standard error is smaller?

Answer 15

It is closer to the population mean

Question 16

What happens if you get a sample mean that is lower than the lowest raw score?

Answer 16

It is not possible

Question 17

How do you find the mean of means?

Answer 17

taking the determined means adding them up and then dividing them by the frequency numbers

Question 18

A distribution of sample means gives us ______ possible sample means, and the frequency with which they occur.

Answer 18

all

Question 19

What is the central limit theorem?

Answer 19

if you have any shape of distribution, and you draw large random samples from the population, then the distribution of the sample means will approach a normal distribution

Question 20

What does the central limit additionally state?

Answer 20

Mean of the distribution of sample means will be equal to the mean of pop, standard error will be equal to standard deviation of pop / by square root of sample size

Question 21

What do you need to know to use the central limit theorem?

Answer 21

Mean (u) sd (o) of the pop of scores, and n

Question 22

What is the first part of the central limit theorem?

Answer 22

Distribution of sample means approaches normal curve as n approaches infinity

Question 23

What is the second part of the central limit theorem?

Answer 23

Mean of distribution of sample means has same value as mean of pop

Question 24

What is the third part of the central limit theorem?

Answer 24

Standard error of mean is standard deviation of known pop divided by square root of n

Question 25

What are the three things that the central limit theorem tells us?

Answer 25

Shape, central tendency, and variability

Question 26

What happens if the distribution of raw scores is not normally distributed?

Answer 26

Need reasonable sample size to obtain the normal distribution

Question 27

What is the value that the differences between distribution of sample means and true normal curve are not substantial?

Answer 27

Once sample gets to 30 data points

Question 28

Will the standard error of the mean always be less than the standard deviation?

Answer 28

Yes

Question 29

What happens with means of the same population?

Answer 29

More similar than raw values

Question 30

The mean of a population of IQ scores is 100. What is the mean of the distribution of sample means for samples of size 64?

Answer 30

100

Question 31

Which formula is appropriate only for use with raw scores?

Answer 31

Z-score (z= (x-u)/o

Question 32

What is the z-score formula for sample means?

Answer 32

z= (xbar- ubar)/(standard deviation bar)

Question 33

What is the explanation for the updated z-score formula?

Answer 33

distribution of sample means (μx̄ ) and divide that by the standard error of the mean (σx̄ )

Question 34

How do you get the area between the z-score and the mean?

Answer 34

subtract the area to the left of our z-score of -1.43 from .5000 (50%) to obtain the area between the z-score and the mean.

Question 35

When do you use the normal approximation of the binomial?

Answer 35

if it can be assumed to follow a normal distribution

Question 36

When can you use the normal approximation of the binomial?

Answer 36

the product of the number of trials n and the probability of a success and of a failure on a given trial are both equal to five or more.

Question 37

Is a binomial distribution discrete?

Answer 37

Yes, consists of successes and failures

Question 38

What is a discrete variable?

Answer 38

Indivisible no half values

Question 39

Is the normal distribution continuous?

Answer 39

Yes.

Question 40

What is a random sampling distribution?

Answer 40

All possible values for any given statistic when we take random samples of same size from pop

Question 41

What does the sampling distribution represent?

Answer 41

Every possible sample you can take when sampling with replacement

Question 42

What is the expected value of the sampling distribution?

Answer 42

Mean of sampling will be = to mean of pop