Practice Exercises for Basic Statistical Concepts
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Identify each of the following as a variable or a constant:
1. an individual's attitude toward abortion at a specific point in time
2. the number of days in February
3. peoples' opinion of the death penalty
4. a student's semester GPA at beginning of semester
5. the number of hairs on someone's head
6. the time it takes to complete a homework assignment
7. a student's semester GPA at the end of the semester
8. The number 12
Identify each of the following as a qualitative or a quantitative variable.
1. a person's name
2. goals scored a hockey team
3. length of a rope
4. shoe color
5. movie titles
6. duration of a movie
7. number of licks to get to the center of a Tootise Roll pop
8. University attended
9. brain activity as measured via EEG
10. camera price
1. A variable that is unrelated to a study, can be controlled, but is often allowed to “randomly vary,” because it does not affect the outcome of the study, is a_____ .
2. In an experimental design, the effect of the_____variable should be seen on the_____variable.
3. The null hypothesis predicts that...
4. An alternative hypothesis predicts that....
5. A population is...
6. A sample is a...
Dr. Logan is interested in the relationship between playing violent video games and aggression in adolescent males. He randomly selects 1000 adolescent males from around New York city and administers a survey for the types of video games that each adolescent male likes to play. He then obtains measures of each adolescent male's aggression by asking each adolescent male's teacher to provide a "toughness rating" on a scale from 1 to 10. The average toughness rating for these adolescent males is 4.56
1. The population is...
2. The sample is the...
3. Say that "Timmy," one of the adolescent males, scores a 7 on the toughness rating. This value of 7 is a...
4. The average toughness rating is a...
5. Is the types of video games that each adolescent male likes to play a qualitative or quantitative variable?
Dr. Smith wants to determine whether playing music during class causes statistics students to pay more attention. He has three stats classes with 40 students/class. For one semester he teaches his morning class while playing Snoop Dogg, in his afternoon class he plays Dio and in his night class he plays no music (a control). During each class meeting, Dr. Smith counts the number of students that fall asleep. He finds an average of 6 students per meeting fall asleep in his morning class, 2 students per meeting fall asleep in his afternoon class and 5 students per meeting fall asleep in the night class.
1. The “population” in this scenario is...
2. The “sample” in this scenario is...
3. In one of Dr. Smith’s night classes, he counts 14 students that fall asleep. This number is...
4. The average of 6 students that fall asleep in the morning class is...
5. The use of different music in each class is a...
6. Counting the number of students that fall asleep uses what kind of measurement scale?
7. Before Dr. Smith can draw any conclusions about the effect of music on statistics student’s paying attention in class, Dr. Smith will need to use...
1. Constant - An individual's attitude toward abortion cannot change at a specific point in time, but can change over time.
2. Variable - February can have 28 or 29 days
3. Variable - Everyone has a different opinion
4. Variable - Your GPA will be influenced by how well you do during the semester and can change depending on your grades.
5. Variable - Hairs grow and fall out all of the time
6. Variable - A homework assignment may take a little or a long time, depending on how well you know the material.
7. Constant - Once the GPA is know, it cannot be changed.
8. Constant - A 12 is a 12 is a 12 and does not change.
1. qualitative
2. quantitative
3. quantitative
4. qualitative
5. qualitative
6. quantitative
7. quantitative
8. qualitative
9. quantitative
10. quantitative
Answers are in underlined in bold italics:
1. A variable that is unrelated to a study, can be controlled, but is often allowed to “randomly vary,” because it does not affect the outcome of the study, is a extraneous variable .
2. In an experimental design, the effect of the independent variable should be seen on the dependent variable.
3. The null hypothesis predicts that there will be no difference between the expected and the observed outcomes; that is, the predicted result will not be obtained.
4. An alternative hypothesis predicts that there will be a difference between the expected and the observed outcomes; that is, the predicted result will be obtained.
5. A population is all member of a target group.
6. A sample is a a subset selected randomly from the target group.
Answers are in underlined in bold italics:
1. The population is all adolescent males, but it could be restricted to all adolescent males living in New York.
2. The sample is the the 1000 adolescent males living in New York that Dr. Logan surveys.
3. Say that "Timmy," one of the adolescent males, scores a 7 on the toughness rating. This value of 7 is a measurement, or a datum, or a raw data point.
4. The average toughness rating is a sample statistic, or a descriptive statistic.
5. Is the types of video games that each adolescent male likes to play a qualitative or quantitative variable? Qualitative
Answers are in underlined in bold italics:
1. The “population” in this scenario is all statistic students.
2. The “sample” in this scenario is the students in Dr. Smith's three statistics classes.
3. In one of Dr. Smith’s night classes, he counts 14 students that fall asleep. This number is a measurement, a raw data point, or a datum.
4. The average of 6 students that fall asleep in the morning class is d descriptive statistic, or a sample statistic.
5. The use of different music in each class is a independent variable.
6. Counting the number of students that fall asleep uses what kind of measurement scale? Ratio, because you can have a value of zero and negative frequencies would be impossible.
7. Before Dr. Smith can draw any conclusions about the effect of music on statistics student’s paying attention in class, Dr. Smith will need to use inferential statistics.