Statistics Chapter 1

What is the value of ΣX2 for the following scores?

21

What is the value of (ΣX)2 for the following scores? Scores: 1, 0, 2, 4

49

What is the value of (ΣX)2 for the following scores? Scores: 1, 5, 2

64

Define the concept of "sampling error." Note: Your definition should include the concepts of sample, population, statistic, and parameter.

A parameter is a value that is obtained from a population of scores and us used to describe the population. A statistic is a value obtained from a sample and used to describe the sample. Typically it is impossible to obtain measurements for an entire population, so researchers most rely on information from samples; that is, researchers use statistics to obtain information about unknown parameters

65. For the following scores, X2 = (X)2. Scores: 1, 1, 1, 1

False

A discrete variable must be measured on a nominal or an ordinal scale.

False

A recent report concluded that children with siblings have better social skills than children who grow up as an only child. This is an example of an experimental study.

False

A researcher interested in vocabulary development obtains a sample of 3-year-old children to participate in a research study. The average score for the group of 20 is an example of a parameter.

False

You are instructed to subtract four points from each score and find the sum of the resulting values. How would this set of instructions be expressed in summation notation?

Sum(X-4)

You are instructed to subtract four points from each score, square the resulting value, and find the sum of the squared numbers. How would this set of instructions be expressed in summation notation?

Sum(X-4)²

Which of the following is an example of a discrete variable?

The gender of each student in a psychology class

Statistical techniques are classified into two major categories: Descriptive and Inferential. Describe the general purpose of each category.

The purpose of descriptive statistics is to simplify the organization and presentation of data. The purpose of inferential statistics is to use looked data from a sample as the basis for making general conclusions about the population

For the following scores, Σ(X + 1) = 9. Scores: 1, 3, 0, 1

True

In an introductory theater class, the professor records each student's favorite movie from the previous year. The teacher is measuring a discrete variable.

True

Recording the number of students who are absent each day at a high school would be an example of measuring a discrete variable.

True

Students in an introductory art class are classified as art majors and non-art majors. This is an example of measurement on a nominal scale.

True

The first step in computing Σ(X + 1), is to add 1 point to each score.

True

The goal for an experiment is to demonstrate that changes in one variable are responsible for causing changes in a second variable.

True

To compute (ΣX)2, you first add the scores, then square the total.

True

For a research study comparing attitude scores for males and females, participant gender is an example of what kind of variable?

a quasi-independent variable

Calculate each value requested for the following set of scores. Scores: 1, 2, 0, 4

a. 7 b. 21 c. (7)2 = 49

What is the first step to be performed in the following mathematical expression? (ΣX)2

add the scores

If it is impossible to divide the existing categories of a variable, then it is an example of a _____ variable

dependent

Statistical methods that organize, summarize, or simplify data are called _______.

descriptive statistics

After measuring two individuals, a researcher can say that Tom's score is 4 points higher than Bill's. The measurements must come from a(n) _______ scale.

interval or ratio

Determining the class standing (1st, 2nd, and so on) for the graduating seniors at a high school would involve measurement on a(n) _____ scale of measurement.

ordinal

Using letter grades (A, B, C, D, and E) to classify student performance on an exam is an example of measurement on a(n) _______ scale of measurement.

ordinal

A researcher is curious about the average monthly cell phone bill for high school students in the state of Florida. If this average could be obtained, it would be an example of a ______.

parameter

Determining a person's reaction time (in milliseconds) would involve measurement on a(n) _____ scale of measurement.

ratio

A researcher is interested in the eating behavior of rats and selects a group of 25 rats to be tested in a research study. The group of 25 rats is an example of a ______.

sample

A researcher uses an anonymous survey to investigate the study habits of American college students. Based on the set of 56 surveys that were completed and returned, the researcher finds that these students spend an average of 4.1 hours each week working on course material outside of class. For this study, the set of 56 students who returned surveys is an example of a(n) _______.

sample

Although a research study is typically conducted with a relatively small group of participants known as a _________, most researchers hope to generalize their results to a much larger group known as a _________.

sample, population

The average verbal SAT score for the entire class of entering freshmen is 530. However, if you select a sample of 20 freshmen and compute their average verbal SAT score you probably will not get exactly 530. What statistical concept is used to explain the natural difference that exists between a sample mean and the corresponding population mean?

sampling error

What is the final step to be performed in the following mathematical expression? (ΣX)2?

square the sum of the scores

A researcher records the change in weight (gain or lost) during the first semester of college for each individual in a group of 25 freshmen, and calculates the average change in weight. The average is an example of a _______.

statistic

A researcher uses an anonymous survey to investigate the study habits of American college students. Based on the set of 56 surveys that were completed and returned, the researcher finds that these students spend an average of 4.1 hours each week working on course material outside of class. For this study, the average of 4.1 hours is an example of a(n) _______.

statistic

A characteristic, usually a numerical value, that describes a sample is called a _______.

statistics

What is the final step to be performed when computing Σ(X - 2)2?

sum the squared values

For an experiment comparing two methods for teaching social skill training to autistic children, the independent variable is _______ and the dependent variable is _______.

teaching methods, the social skills that are learned

A researcher conducts an experiment to determine whether moderate doses of St. Johns Wort have any effect of memory for college students. For this study, what is the independent variable?

the amount of St. Johns Wort given to each participation

What additional information is obtained by measuring two individuals on an interval scale compared to a ordinal scale?

the size of the difference

Calculate each value requested for the following set of scores. Scores: 5, 2, 4, 2

75. a. 11 b. 5 c. 13

31. What is the value of ΣX + 1 for the following scores? Scores: 1, 0, 2, 4

8

To determine how much difference there is between two individuals, you must use either an interval or a ratio scale of measurement.

True

The relationship between a statistic and a parameter is the same as the relationship between ______.

a sample and a population

An experimental research study typically involves measuring two scores for each individual in one group of participants.

False

Classifying people into two groups on the basis of gender is an example of measurement on an ordinal scale.

False

For the following scores, Σ(X + 1)2 = 81. Scores: 1, 3, 0, 1

False

For the following scores, Σ(X - 1) = 10. Scores: 1, 3, 7

False

For the following scores, ΣX2 = 49. Scores: 1, 4, 2, 0

False

What is the value of Σ(X + 1) for the following scores? Scores: 1, 0, 1, 4

14

What is the value of Σ(X + 1) for the following scores? Scores: 2, 4, 7.

16

In a correlational study

2 variables are measured and there is only 1 group of participants

What is the value of Σ(X - 2) for the following scores? Scores: 2, 3, 5

4

In an experimental study

1 variable is measured and 2 groups are compared

What is the value of Σ(X - 1)2 for the following scores? Scores: 1, 2, 1, 4

10

What is the value of Σ(X - 2 )2 for the following scores? Scores: 2, 3, 5

10

What is the value of ΣX + 1 for the following scores? Scores: 1, 6, 3

11

The average score for a population is an example of a statistic.

False

The participants in a research study are classified as high, medium, or low in self-esteem. This classification involves measurement on a nominal scale.

False

Using the average score to describe a sample is an example of inferential statistics. (T/F)

False

A correlational study is used to examine the relationship between two variables but cannot determine whether it is a cause-and-effect relationship.

True

A correlational study typically uses only one group of participants but measures two different variables (two scores) for each individual.

True

A data set is described as consisting of n = 15 scores. Based on the notation being used, the data set is a sampl

True

A high school gym teacher records how much time each student requires to complete a one-mile run. This is an example of measuring a continuous variable

True

A recent report concluded that college graduates have higher life-satisfaction scores than individuals who do not receive college degrees. For this study, graduating versus not graduating is an example of a quasi-independent variable.

True

A researcher is interested in the average income for registered voters in the United States. The entire group of registered voters is an example of a population. (T/F)

True

For statistical purposes, there usually is not much difference between scores from an interval scale and scores from a ratio scale.

True

For the following scores, ΣX2 = 35 . Scores: 1, 3, 5

True

If a researcher measures two individuals on a nominal scale, it is impossible to determine which individual has the larger score.

True

If a researcher measures two individuals on an ordinal scale, then it is impossible to determine how much difference exists between the two people.

True

Describe the sequence of mathematical operations that would be used to evaluate each of the following expressions.

a. To compute ΣX2, you first square each score, then sum the squared values. b. To compute (ΣX)2, you first sum the scores, then square the sum. c. To compute ΣX 2, you first sum the scores, then subtract 2 from the sum. d. To compute Σ(X - 2) you first subtract 2 from each score, then sum the resulting values. e. To compute Σ(X - 2)2, you first subtract 2 from each score, then square the resulting values, then sum the squared numbers.

A researcher uses an anonymous students to investigate the study habits American college students. The entire group of American college students is an example of a(n)

population

Which of the following is an example of a continuous variable?

the amount of time to solve a problem

A recent study reports that elementary school students who were given a nutritious breakfast each morning had higher test scores than students who did not receive the breakfast. For this study, what is the independent variable?

whether or not a breakfast was given to the students