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WEEK 1 Problems
Chapters 1-3
Ch. 1 Intro. to Statistics
Ch.2 Frequency Distributions
Ch. 3 Measures of Central Tendency & Variability
Packet
Pages:
Chapters:
Ch. 1 Intro. to Statistics
Ch. 2 Frequency Distributions
Ch. 3 Measures of Central Tendency & Variability
Refer to the Resource Page on CANVAS for:
StatSheets
Online calculator/statistical app links & tutorials
Using Excel data analysis tutorial
WEEK 1 Problems CH 1-3
1-5
6-12
13-17
Chapter 1
Intro. to Statistics
Defining Key Terms:
Provide brief definitions for the following key terms:
STATISTICS:
VARIABLES:
CORRELATIONAL DESIGN:
PREDICTOR VARIABLE:
CRITERION VARIABLE:
EXPERIMENTAL DESIGN:
INDEPENDENT VARIABLE:
DEPENDENT VARIABLE:
RANDOM ASSIGNMENT:
QUASI-EXPERIMENTAL DESIGN:
EXPLANATORY VARIABLE:
Week 1 Problems CH 1-3
Page 1 of 17
OUTCOME VARIABLE:
NOMINAL LEVEL NUMBER:
ORDINAL LEVEL NUMBER:
INTERVAL LEVEL NUMBER:
RATIO LEVEL NUMBER:
POPULATION:
SAMPLE:
PARAMETER:
STATISTIC:
DESCRIPTIVE STATISTIC:
INFERENTIAL STATISTIC:
Week 1 Problems CH 1-3
Page 2 of 17
Ch. 1-
Explanatory and Outcome Variables
For each of the following experiments, indicate the explanatory and outcome variables.
(see textbook/e-book pp. 12-14).
Example:
Reiser investigated the influence of personality on Facebook use. He had 100 students take a
personality inventory and sorted them into extroverts and introverts. He then had them report
how many hours per week they spent on Facebook.
Answer:
Explanatory Variable = Personality Type (1. Extroverts, 2. Introverts)
Outcome Variable= # of hours per week spent on Facebook
– – – – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – 1. Bentley hypothesized that students who had more experience with the Internet
would adjust better to the first year of college. He gathered 20 first-year college
students; half had maintained their own Web site before coming to college, and half
had no idea how to build a Web site before college. He compared the GPAs of the
two groups.
EXPLANATORY VARIABLE:
OUTCOME VARIABLE:
2. Slotterback & Jones investigated how age influenced attitudes toward the elderly.
They had children, teenagers, young adults, and older adults list as many positive
things as they could think of about “old people.” The number of positive things
listed was counted for each participant.
EXPLANATORY VARIABLE:
OUTCOME VARIABLE:
3. Psych Club wants to know the best way to study for the verbal GREs. To help the club,
you set up several study groups. One group reads a novel every month for a year. A
2nd group studies 20 new vocabulary words each month for a year. A 3rd group takes a
practice verbal GRE each month for a year, and a fourth group is used as a control.
Each participant takes the GRE at the end of the year. Their scores are compared.
EXPLANATORY VARIABLE:
OUTCOME VARIABLE:
Week 1 Problems CH 1-3
Page 3 of 17
Ch. 1-
Measurement Practice
For the following, name the scale of measurement: nominal, ordinal, interval, or
ratio. (see textbook/e-book pp. 16-21).
Example:
Number of Facebook friends.
Answer:
Ratio. Has intervals and provides information about more/less of an attribute, and has an
absolute zero point. (A person could have no Facebook friends).
– – – – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – –
1. Annual Income in Dollars
SCALE:
2. Marital Status
SCALE:
3. Rating of Degree of Enjoyment on a Five-Point Scale
SCALE:
4. IQ Scores
SCALE:
5. Number of Parking Tickets
SCALE:
6. Class Rank
SCALE:
Week 1 Problems CH 1-3
Page 4 of 17
Ch. 1- Identifying Independent Variables, Dependent Variables,
& Number of Treatment Conditions/Levels
For the following Experiments, identify the INDEPENDENT VARIABLE, DEPENDENT VARIABLE,
& NUMBER OF TREATMENT CONDITIONS/LEVELS OF INDEPENDENT VARIABLE.
(see textbook/e-book pp. 9-13).
Example:
A researcher thought money incentive might have an impact on performance on a reading
comprehension test. Subjects were randomly assigned to one of three groups, No money ($0),
$1.00, or $10.00 as an incentive for a certain level of reading comprehension performance. The
researcher found that those participants receiving $10.00 scored significantly higher on the test
compared to the other groups (those getting No money or $1.00).
Answer:
Independent Variable = Amount of money being offered as an incentive.
Levels = 1. No money ($0), 2. $1.00, 3. $10.00
Dependent Variable = Reading Comprehension Test performance
Experiment 1
An investigator wants to compare the top 4 toothpaste brands on the market. He
randomly assigns 200 children participants to the four toothpaste groups, calling them
“Brand A”, “Brand B”, “Brand C” and “Brand D”. Twelve months later, the investigator
compares the average number of cavities between the 4 groups of children, to determine
if one group has fewer cavities.
INDEPENDENT VARIABLE:
LEVELS/CONDITIONS:
DEPENDENT VARIABLE:
Experiment 2
A Social Psychologist was interested in factors that might influence the amount of money a
person decided to donate to a charity. The Psychologist predicted that participants in a
study would donate more money if the request was made publicly (in front of other people)
rather than privately. Subjects were randomly assigned to either a Public Request or
Private Request condition. The researcher compared average amount donated between
the two groups to see if there was a difference.
INDEPENDENT VARIABLE:
LEVELS/CONDITIONS:
DEPENDENT VARIABLE:
Week 1 Problems CH 1-3
Page 5 of 17
Chapter 2
Frequency Distributions
Defining Key Terms:
Provide brief definitions for the following key terms:
FREQUENCY DISTRIBUTION:
GROUPED FREQUENCY DISTRIBUTION:
CUMULATIVE FREQUENCY:
CUMULATIVE PERCENTAGE:
DISCRETE NUMBERS:
CONTINUOUS NUMBERS:
REAL LIMITS:
BAR GRAPHS:
HISTOGRAM:
FREQUENCY POLYGON:
MODALITY:
SKEWNESS:
Week 1 Problems CH 1-3
Page 6 of 17
POSITIVE SKEW:
NEGATIVE SKEW:
KURTOSIS:
Week 1 Problems CH 1-3
Page 7 of 17
Ch. 2-
Construct a Frequency Distribution Table
Use the blank table below to construct a frequency distribution for the following set of 15 scores.
Include columns showing:
• the proportion (p)
• the percentage (%) associated with each score
• and totals
(see textbook/e-book pp. 39-49)
Example:
– – – – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – –
PROBLEM:
Score:
3, 4, 3, 2, 5, 3, 2, 1 , 2, 5, 3, 4, 4, 2, 3
Value
(x)
Frequency
(f)
Proportion
(p)
Percentage
(%)
TOTAL
Week 1 Problems CH 1-3
Page 8 of 17
Ch. 2- Graphing Frequency Distributions: Bar Chart
Following the guidelines on pages 55 and 56 of your textbook, make a bar graph of the following
frequency distribution.
Example:
– – – – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – –
PROBLEM:
Grade:
Students:
A
4
Week 1 Problems CH 1-3
B
12
C
10
D
3
F
1
Page 9 of 17
Ch. 2- Graphing Frequency Distributions: Histogram
Following the guidelines on pages 56 and 57 of your textbook, make a histogram for the
following grouped data.
Example:
– – – – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – — – – – – – – – – –
PROBLEM:
Scores (x)
Freq. (f)
79.5–89.5
69.5–79.5
59.5–69.5
49.5–59.5
39.5–49.5
29.5–39.5
19.5–29.5
9.5–19.5
5
15
6
7
6
15
4
4
Week 1 Problems CH 1-3
Page 10 of 17
Ch. 2-
Interpreting Tables & Graphs: Frequency Distribution Table
Use the information from the 2019 Arizona Department of Transportation
“Traffic Crash Facts” table below to answer the following questions:
Question 1
What Driver Age Group accounts for the highest percentage of All Alcohol Related
Crashes in Arizona? What is the percentage?
ANSWER:
Question 2
What are the top 3 Driver Age Groups for Fatal Alcohol Related Crashes in Arizona? What
are the percentages for each?
ANSWER:
Week 1 Problems CH 1-3
Page 11 of 17
Ch. 2-
Interpreting Tables & Graphs: Frequency Polygon
Use the information from the table below to answer the following questions:
Question 1
What Time of Day on Weekends has the highest frequency for Fatal Crashes? What is the
2nd highest frequency?
ANSWER:
Question 2
What Time of Day on Weekends has the highest frequency for All Crashes? What is the
2nd highest frequency?
ANSWER:
Week 1 Problems CH 1-3
Page 12 of 17
Chapter 3
Measures of Central Tendency & Variability
Defining Key Terms:
Provide brief definitions for the following key terms:
CENTRAL TENDENCY:
VARIABILITY:
MEAN:
VARIANCE:
DEVIATION SCORE:
SUM OF SQUARES:
OUTLIER:
MEDIAN:
MODE:
RANGE:
INTERQUARTILE RANGE:
STANDARD DEVIATION:
Week 1 Problems CH 1-3
Page 13 of 17
Ch. 3
Computation of the Mean, Median & Mode
For each data set below, calculate the: Mean, Median & Mode. Then graph the distribution of
scores. Compare the shape of the distribution to the relative values of the three measures of
central tendency. (see textbook/e-book pp. 79-88).
Check the Resource Page for links to online calculators & instructions on how to use Excel to
calculate the mean, median and mode.
Example:
Data Set: 16,1,2,2,5,10,1,4,5,20,1
N=11 cases
MEAN: Σx/n = 67/11 = 6.09
MEDIAN: Step 1 – order the cases: 1, 1, 1, 2, 2, 4, 5, 5, 10, 16, 20
Step 2 – if odd # of cases, take middle case that cuts distribution in half. The median = 4.
If even # of cases, add the 2 middle scores together & divide by 2 to find midpoint.
MODE: Is the most frequent score. For this data set the mode is 1.
DATA SET 1
2,3,4,7,9,10,5,7,4,5,5
Week 1 Problems CH 1-3
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DATA SET 2
16,1,12,2,15,10,11,14,15,15
Week 1 Problems CH 1-3
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Ch. 3-
Computation of the Mean & Standard Deviation, & Identifying Variables
A study examines the relationship between level of STRESS and PROBLEM-SOLVING ABILITY. The
researcher believes that people who are too “stressed out” will perform more poorly on a task.
The researcher is also interested in the exact degree of stress that might lead to best or worst
performance. To investigate this, the researcher randomly assigns subjects to 1 of 3 treatment
conditions: 1. low stress, 2. moderate stress, or 3. high stress, and manipulates circumstances in
the research scenario to cause subjects to fall into each of the 3 stress conditions. The researcher
then measures the number of problems successfully solved by each subject during a problemsolving task.
Subjects scores on the problem-solving task:
Group 1
LOW STRESS
N=10
2
6
5
7
5
5
4
4
7
6
Group 2
MOD. STRESS
N=10
20
17
12
16
18
19
17
16
18
17
Group 3
HIGH STRESS
N=10
9
8
8
6
7
10
6
8
7
8
IN THIS STUDY:
HINT:
• See Stat Sheet Chapter 3 for
Formulas & computation steps.
• See Resource page for links to
online calculators & other
analysis tools to help with
computations.
ANSWER:
1. What is the INDEPENDENT VARIABLE?
2. What are the LEVELS of the INDEPENDENT VARIABLE?
3. What is the DEPENDENT VARIABLE?
WHAT IS THE:
Group 1
LOW STRESS
Group 2
MOD. STRESS
Group 3
HIGH STRESS
4. MEAN score
5. HIGH/LOW SCORES
6. STANDARD DEVIATION
IN THIS STUDY:
7. Which group performed BEST on the problem-solving task?
ANSWER
8. Which group varied the most in performance on the task?
Week 1 Problems CH 1-3
Page 16 of 17
Ch. 3-
Understanding Research Studies: Mean & Standard Deviation
Use the information from the research study below to answer the questions:
Excerpt from the research study:
The authors assessed the short-term effectiveness of a Web-based alcohol education program on
entering freshmen. Study participants were incoming 1st-year students at a midsized, rural, elite,
private university in the Northeast. The researchers conducted a pre-test and post-test on both the
Control Group and the Intervention Group. The Intervention Group received the Web-based
alcohol education program.
IN THIS STUDY:
ANSWER
1. On the average, which group had higher pretest scores?
2. On the pretest, which group had greater variability in their
scores?
3. On the posttest, which group had less variability in their
scores?
4. On the average, which group showed a greater gain from
pretest to posttest? Explain
Week 1 Problems CH 1-3
Page 17 of 17

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