chapter five-text

Question 1

z-score formula for a population

Answer 1

z = (X-μ)/σ

Question 2

formula to determine a raw score (X) from a z-score

Answer 2

X=μ+zσ

Question 3

z-score formula for a sample

Answer 3

z = (X-M)/s

Question 4

positive v negative z-score

Answer 4

positive - +x points above the mean
negative- -x points below the mean

Question 5

what is the mean in z-scores?

Answer 5

the mean has a z-score of 0

Question 6

in a population with μ=70 and a score of X=68 corresponds to a z-score of z=-.50. what is the population standard deviation?
a. 1
b. 2
c. 4
d. cannot be determined without additional information

Answer 6

c. 4

Question 7

in a sample with a standard deviation of s=4, a score of X=64 corresponds to z=-.50. what is the sample mean?
a. M=62
b. M=60
c. M=66
d. M=68

Answer 7

c. M=66

Question 8

in a population of scores, X=50 corresponds to z=+2.00 and X=35 corresponds to z=-1.00. what is the population mean?
a. 35
b. 40
c. 37.5
d. 45

Answer 8

b. 40

Question 9

in a sample, X=70 corresponds to z=+2.00 and X=65 corresponds to z=+1.00. what are the sample mean and the standard deviation?
a. M=60 and s=5
b. M=60 and s=10
c. M=50 and s=10
d. M=50 and s=5

Answer 9

a. M=60 and s=5

Question 10

formula for the variance for the sample of z-scores

Answer 10

S^2 = (SS)/(n-1)

Question 11

standardized distribution

Answer 11

composed of scores that have been transferred to create predetermined values for μ and σ. they are used to make dissimilar distributions comparable.

Question 12

a population with μ=90 and σ=20 is transformed into z-scores. after the transformation, what is the mean for the population of z-scores?
a. μ=80
b. μ=1.00
c. μ=0
d. cannot be determined from the information given

Answer 12

c. μ=0

Question 13

a sample with a mean of M=70 and a standard deviations of s=15 is being transformed into z-scores. after the transformation, what is the standard deviation for the sample of z-scores?
a. 0
b. 1
c. n-1
d. n

Answer 13

b. 1

Question 14

which of the following is an advantage of transforming X-values into z-scores?
a. all negative numbers are eliminated
b. the distribution is transformed to a normal shape
c. all scores are moved closer to the mean
d. dissimilar distributions can be compared

Answer 14

d. dissimilar distributions can be compared

Question 15

last week sarah had exams in math and spanish. on the math exam, the mean was μ=30 and σ=5 and sarah had a score of X=45. on the spanish exam, the mean was μ=60 with σ=6, and sharah had a score of X=65. for which class should sarah expect the better grade?
a. math
b. spanish
c. the grades should be the same because the two exam score are in the same location
d. there is not enough information to determine which is the better grade

Answer 15

a. math

Question 16

what is the procedure for standardizing a distribution to create new values for the mean and standard deviation?

Answer 16

1. the original scores are transformed into z-scores
2. the z-scores are then transformed into new x-values so that the specific mean and standard deviation are attained

Question 17

a set of scores has a mean of μ=63 and a standard deviation of σ=8. if these scores are standardized sot hat the new distribution has μ=50 and σ=10, what new value would be obtained for a score of X=59 from the original distribution?
a. the score would still be X=59
b. 45
c. 46
d. 55

Answer 17

b. 45

Question 18

a distribution with μ=35 and σ=8 is being standardized so that the new mean and standard deviation will be μ=50 and σ=10. when the distribution is standardized, what value will be obtained for a score of X=39 from the original distribution?
a. X=54
b. X=55
c. X=1.10
d. impossible to determine without more information

Answer 18

b. X=55

Question 19

using z-scores, a sample with M=37 and s=6 is standardized so that the new mean is M=50 and s=10. how does an individual’s z-score in the new distribution compare with his/her z-score in the original sample?
a. new z= old z+13
b. new z= (10/6)(old z)
c. new z= old z
d. cannot be determined with the information given

Answer 19

c. new z = old z

Question 20

for the past 20 years, the high temperature on april 15 has averaged μ=60 degrees with a standard deviation of σ=4. last year, the high temperature was 75 degrees. based on this information, last year’s temperature on april 15 was _______.
a. a little above average
b. far above average
c. above average, but it is impossible to describe how much above average
d. there is not enough information to compare last year with the average

Answer 20

b. far above average

Question 21

a score of x=75 is obtained from a population. which set of population parameters would make x=75 an extreme, unrepresentative score?
a. μ=65; σ=8
b. μ=65; σ=3
c. μ=70; σ=8
d. μ=70; σ=3

Answer 21

b. μ=65; σ=3

Question 22

under what circumstances would a score that is 20 points above the mean be considered an extreme score?
a. when the mean is much larger than 20
b. when the standard deviation is much larger that 20
c. when the mean is much smaller than 20
d. when the standard deviation is much smaller than 20

Answer 22

d. when the standard deviation is much smaller than 20