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Psychology 292 - Introductory Statistics
Assignment #2 – Chi Square, Single Sample, Dependent Samples, and Independent Samples T
Due: Tuesday, April 2, 2013 by Noon
Instructions: For the following questions complete the problems either by hand or using SPSS as
indicated. For problems completed with SPSS, be sure to include all relevant SPSS outputs and highlight
all relevant information in those outputs. You can copy and paste outputs from SPSS into Microsoft
Word if you wish to type your answers. Your conclusions should be written in APA format.
1. The moon illusion is explained as the perception that the moon appears larger when it is seen at the
horizon than when it appears higher in the sky. A study similar to Kaufman and Rock (1962) was
performed where participants were asked to view photographs of the moon on the horizon and then to
draw a circle showing the diameter of the moon that they viewed after the photograph had been
removed. Ten participants performed the task and researchers then measured the diameter of the
circles the participants had drawn. These values were represented as a ratio compared to the actual
size of the moon in the image. Their data is as follows:
1.73
1.13
1.06
1.41
2.03
1.73
1.40
1.63
0.95
1.56
a. What are the alternate and null hypotheses for this question? (Symbols or words) (hint: what
would the ratio be if there was no effect?)
Alternate: The moon illusion is in fact effecting the participant’s idea of the size of the
moon.
Null: The moon illusion does not take any effect on participant’s idea of the size of the
moon.
b. What type of test will you use? Why?
A Single Samples T-Test because we have one set of data and it is compared to a known
parameter.
c. Using SPSS, perform the appropriate test to determine if these data provide evidence of such
an illusion. α = .05 (two-tailed)
A Single-Sample t-test was performed and a significant difference was found, t(9)=4.298,
p<0.003. It was found that the moon watchers did in fact draw the moon larger
(M=1.4630, SD=0.3407) than the parameter (1).
2. A researcher wanted to determine whether army technicians’ ability to track targets on a cathode ray
tube (CRT) monitor differed under two conditions of visual display: white foreground on a black
background and a yellow foreground on a green background. In a pilot study, a random sample of
eight technicians was selected: all eight were observed under both conditions. To avoid practice
effects, the order of presenting the two conditions was randomized so that half the subjects received
the white-on-black condition first. The number of targets accurately tracked (out of a possible 5) is
shown below.
2
White-on-Black Yellow-on-Green
1
2
1
1
2
4
1
2
2
3
1
4
2
2
3
4
a. What are the alternate and null hypotheses for this question? (Symbols or words)
Alternate: There will be a significant difference in the scores when using the
different colored monitors.
Null: There will be no significant difference in scores due to using the different
colored monitors.
b. What type of test will you use? Why?
A Dependent Samples t-test was used because we had the same participants being
studied under two different conditions.
c. Using SPSS, determine whether there was a significant difference in the number of targets
accurately tracked under the two CRT conditions,  = 0.01. What do you conclude about
the different CRT setups?
t(7)= (-3.211), p<.016 (two-tailed), therefore we fail to reject the null hypothesis that
the yellow on green monitor or the white on black monitor is any more effective than
the other.
d. What would your conclusion have been if we had tested this data using a less stringent
 = 0.05?
t(7)= (-3.211), p<.016 (two-tailed), therefore we reject the null hypothesis and
conclude that the participants scored significantly higher when using the yellow on
green CRT monitor (M=2.75, SD=1.165) than on the white on black CRT monitor
(M=1.63, SD=.744).
3. A French teacher was interested in the effect of “immediate, concrete experience” on learning
vocabulary. He decided to conduct an experiment with volunteers from his beginner French class.
The college was 30 miles from a city that students often visited. As he drove to the city one day, he
made a tape describing, in French, the terrain, signs, distances, and so forth. Some students were
given the tape to listen to while driving (immediate, concrete experience) and the others listened to
the tape in the language laboratory. Students then took a vocabulary test and the numbers of errors
was recorded, these data are reported below:
Listened To Tape While in Laboratory Listened To Tape While in Car
11
9
9
8
3
8
10
12
9
10
7
10
11
5
7
9
7
8
10
5
6
a. What are the alternate and null hypotheses for this question? (Symbols or words)
Alternate: There is a significant relationship between where you learn information and
your score on a test.
Null: There is no relationship between where you learn information and your score on a
test.
b. What type of test will you use? Why?
I will use an Independent Samples t-test, because there are two sets of data that are
independent of one another.
c. Analyze the data in SPSS using the appropriate test (α = 0.05). What is your conclusion about
the effect of immediate, concrete experience?
An Independent Samples T-Test was performed and a significant difference was found,
t(18)=3.2, p.<0.05. Therefore we conclude that the Laboratory condition (M=9.7.
SD=.473) performed significantly better than the Car condition (M=7.4, SD=.542).
4. Many professors do not include a penalty for incorrect answers given on multiple choice questions. A
group of students were given a series of questions related to a reading comprehension passage,
however they were not given the opportunity to read the passage beforehand. Students were
instructed to read through the questions and try to guess the best answer based on the options given.
Each multiple choice question had 5 options.
Student scores (percentages)
58
53
47
45
48
41
33
39
48
60
47
47
41
55
40
50
34
44
46
53
43
43
53
46
38
49
40
53
a. What are the alternate and null hypotheses for this question? (Symbols or words) (hint: what
is the probability of guessing each question correctly?)
Alternate: The students will not perform better than chance.
Null: The students will perform better than chance.
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b. What type of test will you use? Why?
I will use a Single Samples t-test because there is one set of data that is being compared
to the known parameter (100).
c. Analyze the data in SPSS using the appropriate test (α = 0.05). Test the hypothesis that the
students are performing better than chance.
t(27)=(-42.293), p<0.05 (two-tailed), therefore reject the null hypothesis and conclude
that the group of students performed significantly worse (M=46.214, SD=6.73) than if
they had the chance to study first.
5. A study was conducted to determine whether big-city and small-town dwellers differed in their
helpfulness to strangers. In this study, the investigators rang the doorbells of strangers living in
Halifax or small towns in the vicinity. They explained they had misplaced the address of a friend
living in the neighbourhood and asked to use the phone. The following data show the number of
individuals who admitted or did not admit the strangers (the investigators) into their homes:
Big-City
dwellers
Small-Town
dwellers
Helpfulness to Strangers
Admitted
Did not admit
strangers into strangers into
their home
their home
24
36
28
6
a. What are the alternate and null hypotheses for this question? (Symbols or words)
Alternate hypothesis: Where you live does affect your helpfulness to strangers.
Null hypothesis: Where you live does not affect your helpfulness to strangers.
b. What type of test will you use? Why?
Chi-square because we have one or more categorical variables with two or more levels
(where they were from, two options) (if they were helpful, two options).
c. Is there a relationship between dwelling location and helpfulness to strangers? (α = 0.05)
Yes, there is a relationship between the dwelling location and the helpfulness to
strangers.
X2 (1)= 15.750, p<0.001, therefore the participants were not helping strangers according
to chance.
d. Include a bar graph. Verbally describe the results.
As shown in the bar graph, big-city dwellers are more likely to not be helpful to
strangers (green bar), and small-town city dwellers are more likely to be helpful to
strangers (blue bar).
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6. A physics instructor believes that natural lighting in classrooms improves student learning. He
conducts an experiment in which he teaches the same physics unit to two groups of seven randomly
assigned students in each group. Everything is similar for the groups, except that one of the groups
receives the instruction in a classroom that admits a lot of natural light in addition to the fluorescent
lighting, while the other uses a classroom with only fluorescent lighting. At the end of the unity, both
groups are given the same end-of-unit exam. The percentages achieved are below.
Fluorescent lighting Fluorescent and Natural Lighting
75
85
85
92
67
78
77
80
83
88
88
94
86
89
90
a. What are the alternate and null hypotheses for this question? (Symbols or words)
Alternate: There is a significant relationship between learning information in
fluorescent lighting compared to natural lighting.
Null: There is no relationship between learning information in fluorescent lighting or
natural lighting.
b. What type of test will you use? Why?
The type of test that I will use is an Independent sample t-test because we have on
categorical variable (the lighting) and one scale variable (the score), which is tested
using two randomly assigned groups.
c. Analyze the data in SPSS using the appropriate test (α = 0.05). What is your conclusion about
the effect of fluorescent versus natural light?
An Independent Samples t-test was performed, t(13)=2.021, p>0.05 (two-tailed),
therefore fail to reject the null hypothesis and draw no conclusions.
d.
If the results were borderline significant, what could you do to bolster your findings on
subsequent trials?
If the findings were borderline significant, I would increase the number of participants
that I use in subsequent trials. This will increase the amount of data that we have to
work with, therefore increasing or decreasing the significance and giving us more
accurate results.