Reading Quiz 2

Question 1

True or False: the standard score for any observation tells how many standard deviations that score is from the mean.

Answer 1

true

Question 2

What two steps do we do to standardize a score?

Answer 2

subtract the mean and divide by the standard deviation

Question 3

standard score is often called by what other term?

Answer 3

the z-score

Question 4

What does the sign of a standard score correspond to?

Answer 4

its direction: if the z-score is positive it’s above the mean and if it’s negative it’s below the mean

Question 5

The scales of density curves are adjusted so that the total area under each curve is what? A. 1

Answer 5

1

Question 6

The area under the density curves between a couple of x-axis values represents what?

Answer 6

the proportion of all observations that fall between those values

Question 7

Do measures of center and spread apply a to density curve as well as to sets of observations?

Answer 7

yes

Question 8

How do you define the median of the density curve?

Answer 8

the point with half the area under the curve to its left and the remaining half of the area to its right

Question 9

The quartiles of a density curve divide the area into what?

Answer 9

four equal parts

Question 10

What is the relationship between the mean and the median of a symmetric density curve?

Answer 10

they are equal

Question 11

Which is pulled the farther toward the tail of a skewed distribution: the median, or the mean?

Answer 11

the mean

Question 12

In conventional notation, what are the meanings of x and s, as contrasted to  and  ?

Answer 12

the first two refer to the mean and standard deviation, respectively, of a set of observations, a sample. the second two refer to the mean and standard deviation, respectively, of a density curve idealized distribution, or the population distribution

Question 13

What three features describe the overall shape of normal curve?

Answer 13

normal curves are symmetric, single peaked (unimodal), and bell shaped

Question 14

Is there only one normal curve, or is there an infinite number of normal curves?

Answer 14

an infinite number

Question 15

For any given mean and standard deviation, is there only one normal curve, or an infinite number of
normal curves?

Answer 15

only one

Question 16

How can you visually find the points of one standard deviation from the mean of a normal curve?

Answer 16

those points are the inflection points of the curve. there, the curve changes from falling more and more steeply to falling less and less steeply, or vice versa.

Question 17

The distributions of test scores, of measures of characteristics of living things, and of summary statistics for chance outcomes repeated many times, often (but not always!) follow what type of distribution?

Answer 17

normal distribution

Question 18

What three percentages do you have to remember when you are stating the “empirical rule?”
A. 68%, and 95%, and 99.7%.

Answer 18

68%, 95%, 99.7%

Question 19

Are the three percentages for 1, 2, and 3 standard deviations exact, or easier-to-remember rounded approximations?

Answer 19

approximations

Question 20

What do the three percentages in the empirical rule apply to? In other words, what is the meaning of this rule?

Answer 20

the three numbers tell the percent of observations falling within the region plus or minus 1, 2, or 3 standard deviations from the mean, respectively, in a normal curve

Question 21

True or false: If Mary scores one standard deviation above the mean on a normally distributed test, then approximately 68% of the test takers scored as close to the mean of the test as, or closer to the mean than, Mary did.

Answer 21

true

Question 22

True or false: If Mary scores one standard deviation above the mean a on a normally distributed test, her score is in the 68th percentile.

Answer 22

false

Question 23

True or False: if Mary scores one standard deviation above the mean on a normally distributed test, half of 68% or 34% are above the mean but at or below Mary’s score. An additional 50% are below the mean. Thus Mary equals or surpasses 50% plus 34% of the test takers, and is at the 84th percentile.

Answer 23

true

Question 24

What does the notation N(100,15) mean?

Answer 24

it denotes a normal distribution with a mean of 100 and standard deviation 15

Question 25

In a standard normal distribution, what is the value of the sample mean of the z-scores and the sample standard deviation of the z-scores?

Answer 25

sample mean 0

sample standard deviation 1

Question 26

In a table of areas under the standard normal curve, what does the table entry for each z score represent?

Answer 26

the area under the curve to the left of z, or in other words, the proportion of cases with values less than z

Question 27

What steps do you follow with a z table if you want to know what proportion of the scores are between two values?

Answer 27

look up the proportion less than the first, and less than the second, and find the difference between the two proportions

Question 28

What steps do you follow with a z table if you want to know what proportion of the scores are greater than a value?

Answer 28

look up the proportion less than the value then do 1 minus that proportion

Question 29

What do the authors recommend (as a word to the wise for future test-takers) as the last step of problems giving a normal distribution and asking for proportions of observations?`

Answer 29

they recommend stating the conclusion in the context of the problem. thus, rather than just saying the answer is 49%, you would say, “about 49% of boys have cholesterol levels between 170 and 240 mg/dl”

Question 30

What steps do you go through when you want to find a value given a proportion of a normal distribution, using the z-table?

Answer 30

you look for the proportion in the body of the table, and you find at the margin the z-score that corresponds to it. then you unstandaqdize the z-score

Question 31

What operations do you do, and in what order, to “unstandardize” a z-score, or turn the z-score into a raw score?

Answer 31

you multiply the z-score by the standard deviation then you add it to the mean

Question 32

percentiles

Answer 32

measure location relative to median

Question 33

z-scores

Answer 33

measure location relative to mean

Question 34

what to do if you have duplicates

Answer 34

choose highest one

Question 35

standardizing

Answer 35

converting raw data to standard deviation units

gives z-score, tells you how many standard deviations away from the mean the observation falls and in which direction

Question 36

z-score formula

Answer 36

z = (observation - mean)/standard deviation

Question 37

when is the median the highest point

Answer 37

only when the data is symmetric

Question 38

what is the rule called

Answer 38

either 68-95-99.7 rule

or the empirical rule

Question 39

rule

Answer 39

can only use with normal data

Question 40

Density curve

Answer 40

Always lies on or above the horizontal axis
Has area exactly one underneath it
Approximates shape of actual distribution
Most commonly used family of density curves are normal curves

Question 41

Median v mean in density curve

Answer 41

Median divides area under curve ni half

Mean is point at which curve would balance if it was made of solid material

Question 42

Standard normal distribution

Answer 42

N(0, 1)