Review for Exam 2
1) In a planned study, here is a known population with a normal distribution, pop mean =
50, pop standard dev = 5. What is the predicted (standardized) effects size (d) if the
researchers predict that those given an experimental treatment have a mean of
a) 50
b) 52
c) 54
d) 56
e) 47
For each part, also indicate whether the effect is approximately small, medium, or large.
d
1  2 50  50

0

5
d
1  2 52  50

 0.4 medium effect

5
d
1  2 54  50

 0.8 large effect

5
d
1  2 56  50

 1.2 large effect

5
d
1  2 47  50

 0.6

5
no effect
large effect
2) For each study described below indicate:
(i) People with agoraphobia are so filled with anxiety about being in
public places that they seldom leave their homes. Knowing this is a
difficult disorder to treat, a researcher tries a long-term treatment. A
sample of individuals report how often they have ventured out of the
house in the past month. Then they receive relaxation training and are
introduced to trips away from the house at gradually increasing durations.
After 2 months of treatment, subjects report the number of trips out of the
house they made in the last 30 days. The researcher wants to determine if
the number of trips out of the house has increased after the treatment.
(a) one-tailed (“increased after treatment”)
(b)
H0: μpost treatment < μpre treatment
HA: μpost treatment > μpre treatment
(c) What is the appropriate statistical test to compute
related samples t-test
(ii) An experiment studied the effect of diet on blood pressure.
Researchers randomly divided 54 healthy adults into two groups. One
group received a calcium supplement. The other received a placebo. Blood
pressure was measured at the end of one month of supplements or
placebos.
(a) two-tailed “the effect”
(b)
H0: μcalcium supplement group = μplacebo group
HA: μcalcium supplement group ≠ μplacebo group
(c) What is the appropriate statistical test to compute
independent samples t-test
(iii) Suppose that during interpersonal social interactions (e.g., during
business meetings or talking to causal acquaintances) people in the US
maintain an average distance of μ = 7 feet from other people. The
distribution of distance scores is normal with a σ = 1.5 feet. A researcher
examines how the US compares in social interaction distance to social
interaction distance for people in Italy. A random sample of 40 Italians is
observed during interpersonal interactions. For this sample, the mean
interaction distance is 4.5 feet. Do the Italians have closer social
interactions than Americans do?
(a) two-tailed
(b)
H0: μItalian group = μUS group
HA: μItalian group ≠ μUS group
(c) What is the appropriate statistical test to compute
1 sample z-test
(iv) The animal learning course in a university's psychology department
requires that each student train a rat to perform certain behaviors. The
student's grade is partially determined by the rat's performance. The
instructor for the course has noticed that some students are very
comfortable working with the rats and seem to be very successful training
their rats. The instructor suspects that that these students may have
previous experience with pets that gives them an advantage in the class.
To test this hypothesis, the instructor gives the entire class a questionnaire
at the beginning of the course. One question determines whether or not
each student currently has a pet of any type at home. Based on the
responses to this question, the instructor divides the class into two groups
and compares the rats' learning scores for the two groups.
(a) one-tailed (“ these students have an advantage”)
(b)
H0: μexperienced group < μinexperienced group
HA: μexperienced group > μinexperienced group
(c) What is the appropriate statistical test to compute
independent samples t-test
(v) A scientist investigated the authenticity of ESP abilities by asking
subjects who claimed to have ESP abilities to predict the symbol that
would appear on the back side of a succession of cards. Each card had a
square, a circle, a star, or a triangle. Subjects were informed of this fact
and were asked to predict what was on the back of each card as it was held
up to them. Because the subjects could not see the backs of the cards, if
they had no ESP abilities and simply guessed, they would get an average
of .25 answers correct (so μ = .25, σ = 4.5). The scientist measured how
many answers the subjects got correct out of 100 cards.
(a) one-tailed (ESP claim to predict symbol above chance)
(b)
H0: μesp group < μchance group
HA: μesp group > μichance group
(c) What is the appropriate statistical test to compute
1 sample z-test
(vi) A researcher is interested in how values taught to students by their
parents influence their academic achievement. The parents of one group of
students is asked to follow a program where they spend one hour per day
discussing homework assignments with their child. In the other group,
parents are given no program to follow. In order to control for genetic
influences on academic achievement, the subjects in the study are identical
twins raised apart (i.e., by different parents). One of the twins is randomly
assigned to one group and the other twin is placed in the other group.
Academic achievement is measured by GPA at the end of the first year of
high school.
(a) two-tailed “how values influence”
(b)
H0: μprogram group = μno program group
HA: μprogram group ≠ μno program group
(c) What is the appropriate statistical test to compute
related samples t-test
3) On a vocational interest inventory that measures interest in several categories, a very
large standardization group of adults (i.e., a population) has an average score of μ = 22
and σ = 4. Scores are normally distributed. A researcher would like to determine if
scientists differ from the general population in terms of writing interests. A random
sample of scientists is selected from the directory of a national science society. The
scientists are given the inventory, and their test scores on the literary scale are as follows:
21, 20, 23, 28, 30, 24, 23, 19. Do scientists differ from the general population in their
writing interests? Test at the .05 level of significance for two tails.
two-tailed “if scientists differ”
H0: μprogram group = μno program group
HA: μprogram group ≠ μno program group
1 sample z-test (we have one sample, σ is known)
z
z
X
X
X 
23.5  22
 1.06
1.41

n

4
 1.41
8
X
 X =23.5
n
go to table, zcrit = ±1.96
The computed z-score is not within the critical region, so we should fail to reject the H0
and conclude that there is not enough evidence to conclude that scientists differ from the
general population.
4) A marine biologist is comparing the size of Great White Sharks in the Pacific and
Atlantic Oceans to determine which ocean has the larger sharks. He takes a sample of 10
sharks from each ocean and measures their lengths. The measurements are listed below:
Shark Lengths
Pacific Ocean
Atlantic Ocean
18.2
16.1
15.8
14.3
13.6
14.7
19.7
15.7
19.1
19.6
12.2
15.3
16.8
13.2
22.8
15.8
16.6
15.2
16.8
X1 
two-tailed “which has larger sharks”
H0: μpacific = μatlantic
HA: μpacific ≠ μatlantic
independent samples t-test, α = 0.05
t
n
SS  X  X1   82.8
2
X2 
1
 X 2  1   2 
s X1  X2
s X1  X2 
sp 
sp
n1

sp
n2

6
6

 1.1
10 10
SS1  SS2 82.8  25.2

 6.0
df1  df2
99
17.16  15.61
 1.41
1.1
dfT = n1 + n2 – 2 = 18
df1 = n1 – 1 = 9
df2 = n2 – 1 = 9
t
16.2
 X  17.16
X
 X  15.61
n
SS  X  X1   25.2
2
go to table, tcrit = ±2.1
Using the appropriate statistical test, determine if there is a size difference in sharks
between the two oceans, and if there is a difference state which ocean has the larger
sharks. Test at the .05 level of significance.
The computed t-score is not within the critical region, so we should fail to reject the H0
and conclude that there is not enough evidence to conclude that sharks in the two ocean
differ in size.
5) A behavioral psychologist wants to know if food acts as a good motivator for rats to
learn a maze faster than normal. She places a food pellet at the end of a maze that the rat
can smell while working through the maze. She puts 8 rats through the maze and records
how long it takes them to find the food at the end. She already knows that without the
food, rats take an average of 28.9 seconds to run the maze (with a normal distribution).
Using the timing data recorded below, determine if the rats learn the maze faster with the
food pellet than without it. Test at the .01 level of significance.
Times to run maze (n=8): 25.6, 29.0, 23.1, 25.5, 28.7, 26.5, 25.4, 23.9
one-tailed “learn a maze faster than normal”
H0: μwith food group > μwithout food group = 28.9
HA: μwith food group < μwithout food group
1 sample t-test (we have one sample, σ is unknown)
t
X
sX
sX 
s
2.07

 0.73
n
8
X  X 
X
 X = 25.96
n
2
s
t
n 1
25.96  28.9
 4.03
0.73

30.12
 2.07
7
df = n – 1 = 8 – 1 = 7
go to table, tcrit = -2.998
The computed t-score is within the critical region, so we should reject the H0
and conclude that there is enough evidence to conclude that the rats with food were faster
than the general population of rats (without food).
6) Does caffeine reduce depression? Subjects in this study were 10 people diagnosed as
caffeine users (i.e., they regularly consume something containing caffeine each day).
During the study, however, each subject was barred from consuming caffeine not
provided by the experimenter. Subjects came to the lab two subsequent mornings and
were given a pill. The pill either contained caffeine or was a placebo (i.e., each subject
received both pills but on different days). The order of the pill received was
counterbalanced across subjects. Subjects completed a depression scale at the end of each
day. Based on the depression scores below (higher scores mean more depression), does
caffeine appear to reduce depression?
Depression Scores
Caffeine
Placebo
Difference
scores
5
16
-11
5
23
-18
4
5
-1
3
7
-4
8
14
-6
one-tailed “does caffeine reduce depression”
H0: μD > 0
HA: μD < 0 (caffeine – placebo)
related samples t-test, α = 0.05
t
D  D
D
sD 
sD
6.68

 2.11
nD
10
D  D 
2
5
24
-19
0
6
-6
0
3
-3
2
15
-13
11
12
-1
sD 
D
 D  8.2
nD  1

401.6
 6.68
9
nD
8.2  0
t
 3.88
2.11
dfD = nD – 1 = 9
go to table, tcrit = -1.83
The computed t-score is within the critical region, so we should reject the H0
and conclude that there is enough evidence to conclude that caffeine reduced depression.