Angie Predmore, Mike Prentice,
Vida Lozano-Alvarado, Paul Albertine & Andy Arnold
Psyc 281: Stats
Prof. C. Conley
Exam 2 Practice Questions Written by Students
Jennifer, Chie, Abbie, Megan
Ch. 5
1. When and entire distribution of x values is transformed in to z-scores, the z-score distribution will
have:
a. a standard derivative of 1
b. a mean of 0
c. the same shape as the distribution of raw scores
d. all of the above
e. none of the above
Answer: D
2. Which z-score(s) would NOT be considered representative of the population mean?
a. -2.73
b. -0.5
c. 1.84
d. all of the above
e. a and c only
Answer: E
3. A distribution of scores from a test has a mean of µ=75 and a standard derivative of =7. Find the zsores for the following scores:
a. X= 67
b. X= 95
c. X=82
Answer:
a. (67-75)/7= -1.14
b. (95-75)/7= +2.86
c. (82-75)/7= +1.00
4. A distribution of scores forma test has a µ=35 and a =4. Find the X values for each z-score.
a. z=-.39
b. z=+1.11
c. z=-2.9
Answer:
a. x=35+(-.39)(4)= 33.44
b. x= 35+(1.11)(4) = 39.44
c. x= 35+(-2.9)(4) =23.4
Essay. Explain why the z-scores distribution always has a mean of zero and why the distribution of z
score always zero.
Sample Answer: Mean of Zero: because from the original population those scores above the mean
because positives where as those below the mean became negative, thus combined make zero.
Chapter 6:
Angie Predmore, Mike Prentice,
Vida Lozano-Alvarado, Paul Albertine & Andy Arnold
Psyc 281: Stats
Prof. C. Conley
1. The normal distribution contains:
a. mean, median, mode
b. z-scores and probability
c. proportion of cases and percentile rank
d. all of the above
e. none of the above.
Answer D
2. Which is an example of random sampling?
a. selection a sample of students form Psych 281
b. drawing form a deck of cards and keeping the cards out
c. drawing form a jar of jelly beans and putting them back in
d. tossing a weighted coin.
Answer: C
3. The distribution of Colleen’s stats test score is a normal distribution where µ= 77 and = 5.
A. What X separates the top 10% from the rest of the population?
B. What X separates the top 25% from the rest of the distribution?
Answers:
A. 0.1= .4602= z-score
X= µ+z
X= 77+ (.4602)(5)= 79.3
B. 0.25= .4013=z-score
X= µ+z
X= 77+ (.4013)(5) = 79.0006
4. After flipping a two-sided coin a number of times you discover that the coin is weighted so that for
every tail shown 4 heads come up. What is the probability of flipping exactly 50 heads out of 75 flips of
the coin?
Answer: p(tails)(n)=(1/5)(75)=15 p(heads)(n)=(4/5)(75)=60
=(75)(1/5)(4/5) = 12= 3.4661
49.5≤X≤50.5 (Using real limits for discrete number)
Z=(X-µ)/= (49.5-60)/12= -3.031…… in the table = .0012 in the tail
Z=(X-µ)/= (50.5-60)/12= -2.742……. in the table= .0031 in the tail
.0031-.0012= .0019
Essay: When does one use the binomial distribution? Explain and give and example:
Sample Answer: When the measurement procedure classifies individuals into exactly two categories.
Example Heads and Tails.
Ch. 7
1. A distribution of sample means will be perfectly normal is:
a. the population from the which the samples are selected is a normal distribution
b. the population form which the samples are selected has at least N=75 scores
c. the number of scores (n) is each sample is relatively large
d. the number of scores (n) in each sample has at least 35 scores
e. both a and b
f. both a and c
Angie Predmore, Mike Prentice,
Vida Lozano-Alvarado, Paul Albertine & Andy Arnold
Psyc 281: Stats
Prof. C. Conley
g both b and e
h. none of the above
Answers: either A or C (This is one of Abbie’s questions… she refuses to follow the rules of scan-tron)
2. The collection of sample means for all the possible random samples of a particular size (n) that can be
obtained from a population.
a. central limit theorem
b. distribution of sample means
c. sample distribution
d. sample size
Answer: B
3. A population has a =37.
a. if a single score is selected form this population, how close would you expect the score to be to
the population mean?
b. If a sample of n=9 scores is selected from the population, what would the standard error be?
c. If a sample of n=36 scores were selected what would be the standard error?
Answer:
A. The standard deviation = 37, measures the standard distance between the score and the mean.
B. 37/9= 37/3= 12.33
c. 37/36=37/6= 6.167
4. A teacher wants to pick a random sample from a population with a = 10.
A How large of a sample is needed to have a standard error of 5 pts or less?
B. How large of a sample is needed to have a standard error of 1pt. or less?
Answers:
A. 4
B. 100
Essay: Describe the relationship between standard error and the sample distribution, and the causes for
this relationship.
Sample Answer: m and n are inversely related; standard error decreases as the number of sample scores
increases. Mathematically, according to the formula for standard error  will be smaller as  is divided by
a large n. Conceptually each time you compute M for a sample you’re compressing a range of scores into
one central value. The larger the n the more compression o
Erin, Mary, Jarrett
Chapter 5
Multiple Choice:
Q: For a distribution of z-scores, the mean is ____ and the standard deviation is ___.
a) 1,0
b) 2,1
c) 0,1
d) 0,0
A: c) 0,1
Angie Predmore, Mike Prentice,
Vida Lozano-Alvarado, Paul Albertine & Andy Arnold
Psyc 281: Stats
Prof. C. Conley
Q: When a distribution of X values is changed into z-scores the shape will ________.
a) be inverted
b) stay the same
c) cannot be determined given the information provided
A: b) stay the same
Q. Which of the following statements is NOT true of z-scores?
a.) Each z-score will tell the exact location of the original X value within the distribution.
b.) The z-scores will form a standardized distribution but cannot be directly compared to other
distributions that have been transformed into z-scores.
c.) The number of a z-score represents the number of standard deviations existing between the score
and the mean.
d.) The sign (+,-) is very important because it tells whether the z-score is above or below the mean.
b
Q. The transformation of an entire population into z-scores will NOT change _____.
a.) the shape of the scores in a distribution sketch
b.) the mean
c.) the numbers labeling the distribution in the sketch
d.) the standard deviation
a
Q. If = 100 and X = 105 and the corresponding z-score is 2.6, what is the standard deviation (
A. (105-100)/


Q. For a distribution with a mean of  and a standard deviation of , what X value would
correspond with a z-score of 3?
A. X
X X

Computation:
Q: A distribution of scores has a mean of 30 with a standard deviation of 6. Find the z-score for X=42.
A: (42-30)/6= 12/6 = 2
Q: For a distribution of scores that has a mean of 50 and a standard deviation of 5, find the X value that
corresponds to the z-score of 2.
A: (X-50)/5=2
(2*5)+50=10+50=60


Short answer:
Q: What does a z-score measure and why would anyone want to use it.
A: A –score specifies the exact location of X within the distribution. The numerical value of the z-score
specifies the number of standard deviations between X and the mean. The sign (+ or -) indicates whether
X is to the left of right of the mean.
Angie Predmore, Mike Prentice,
Vida Lozano-Alvarado, Paul Albertine & Andy Arnold
Psyc 281: Stats
Prof. C. Conley
Q. Why should we bother converting z-scores if we already have the mean of the raw scores available?
Give an example of a hypothetical situation in which the mean of the raw score is not enough by itself
to demonstrate the exact placement of X in a distribution of scores.


Chapter 7
1) What formula is used to locate each of the sample Means (M) in a distribution?
a) σm = √(σ2/n)
b) z = (M - µ) / (σm)
c) z = (X-pn) / [√(npq)]
d) z = (X - µ) / σ
Q: What does standard error measure and why would you use it?
A: Standard error measures the standard distance between a sample mean and the population.
You would use it to tell how much error to expect if you are using a sample mean to estimate a
population mean.
Q: What is a good sample size?
A) 3
B) 300
C) 30
D) 3000
A: C)30
Sean, Carolyn, Melissa, Al
Chapter 7
1. Standard error is to _______ as standard deviation is to scores:
a. Parameter
b. Sample means
c. Inter-quartile range
d. Probability
b
2. What is the best way to minimize sampling error?
a. More samples
b. More sample scores
c. Less samples
d. More sample means
d
3. Calculate z score when  = 50,  = 6, n = 4, M = 55.
m = /n  6/43
z = M-/m55-50/35/31.67
4. Caclucate the range of scores that are in the middle 30% of the sample means for SAT scores
when  = 500,  = 100, n = 225.
m = /n  100/2256.67
z = M-/m±.39 = M-500/6.67497.40 – 502.60
5. Define standard error graphically, mathematically, and conceptually.
m = /n
Angie Predmore, Mike Prentice,
Vida Lozano-Alvarado, Paul Albertine & Andy Arnold
Psyc 281: Stats
Prof. C. Conley
Standard error is the standard deviation of the distribution of the sample means. The
standard error measures the standard amount of difference between M and 
Mike, Andy, Paul, Vida, Angie
We did this one in class on 2/3
Chapter 5
1. A z-score can perform which of the following functions:
a. Make comparisons between data from two different sets.
b. Can standardize a distribution
c. Describes the exact location of a score.
d. All of the above.
Answer: d
2. The equation for calculating a z-score is:
a. z = (X - μ)/ σ
b. z = X/ σ
c. z = - (X * μ) π
d. z = - (X - μ)/ σ
Answer: a
3. How do z-scores help us understand how normal/abnormal a particular subject is?
Answer: z-scores tell the exact location of each X value within the distribution. Looking at the location
of the z-score for a specific value helps us understand how close the value is to the population mean. In
other words we can tell how well the score represents the population.
4. For a population with μ = 60, a raw score of X = 25.75 corresponds to a z = - 2.00. What is the
standard deviation? (
Answer: σ = 17.125
5. On Monday, Yngwie Malmsteen got a score of X=79 on his math test with μ = 75 and σ = 6. The same
day Lou Diamond Phillips got a score of X = 65 on a math test with μ = 61 and σ = 2. Who should expect
to get a better grade, Yngwie or Lou Diamond? Explain your answer. (
Answer: Lou, his Z-score is higher than Yngwie’s.
Chapter 6
1. What two requirements must a random sample satisfy?
Answer: 1. Each individual in the population must have an equal chance of being selected. 2. if more
than one individual will be selected, a constant probability must exist for every selection.
2. What are the two meanings for the symbol p?
a. Probability and percentage
b. Percentile rank and the probability of B in a binomial distribution
c. Probability of A in a binomial distribution and Probability
d. Proportion of a normal distribution and percentile rank
Answer: c
Angie Predmore, Mike Prentice,
Vida Lozano-Alvarado, Paul Albertine & Andy Arnold
Psyc 281: Stats
Prof. C. Conley
3. What is generally referred to as a good sample size when working with normal data?
a. n = 50
b. n = 250
c. n = 30
d. None of the above
Answer: c
4. Computation: A population forms a normal distribution with μ = 152 and σ = 16. Find the
probability of selecting a score with a value of 125. Answer: 4.55%
5. Computation: For a population, the mean score is 500 with a standard deviation of 100. Find the
score that separates the bottom 5% from the rest of the population. Answer: 336
Chapter 7
1. Explain the difference between standard deviation and standard error. Use examples and formulas
as necessary.
Answer: The standard deviation measures the typical distance of scores from the mean. The standard
error measures the average or standard distance between a sample mean and the population mean.
2. Choose the correct formula for the computation of standard error.
a. σM = σ / √n
b. σM = √n / x
c. σM = √σ / n
d. σM = ∑N / σ
3. Choose the condition(s) necessary to create an almost perfectly normal sample distribution.
a. Samples are large in number (≈30)
b. Samples are selected from a normal distribution.
c. Sample size is at least half of the population size.
d. b,c
e. a,b
Answer: e
4.
A population has a mean of 25 with a standard deviation of 2.3.
For a sample of 40 what is the probability that the mean is between 24.5 and 25.5?
Answer: Find the standard deviation of the sample first.
Standard deviation = 2.3 / square root of 40
Standard deviation = 0.364
Then find the z-scores.
24.5 – 25 / 0.364 = -1.37
25.5-25 / 0.364 = + 1.37
P(24.5 < X < 25.5) = .9147 - .0843 = .8294
Angie Predmore, Mike Prentice,
Vida Lozano-Alvarado, Paul Albertine & Andy Arnold
Psyc 281: Stats
Prof. C. Conley
5. The average mean for a population is 650 with a standard deviation of 420. In a sample of 100 what
is the probability that the mean is greater than 700?
Answer: Standard deviation = 420 / square root of 100 = 42.
Z-scores
(700 – 650) / 42 = 1.19
P( x > 700) = 1 - .8830
= .1170