Question

apply statistical methods and analysis. Unless otherwise stated, use 5% (.05) as your alpha level (cutoff for statistical significance).

#1. What information does a correlation coefficient convey?

#2. State whether each of the following is an example of a positive correlation or a negative correlation.

a. Higher education level is associated with a larger annual income

. b. Increased testosterone is associated with increased aggression.

c. The smaller the class size, the more students believe they are receiving a quality education.

d. Rising prices of apples are associated with the sale of fewer apples.

#3. Which is the predictor variable (X) and which is the criterion variable (Y) for each of the following examples?

a. A researcher tests whether the size of an audience can predict the number of mistakes a student makes during a classroom presentation.

b. A military officer tests whether the duration of an overseas tour can predict the morale among troops overseas. \

c. A social psychologist tests whether the size of a toy in cereal boxes can predict preferences for that cereal.

Answer 1

#1.

The correlation coefficient is a statistical measure that calculates the strength of the relationship between the relative movements of two variables. The values range between -1.0 and 1.0. A calculated number greater than 1.0 or less than -1.0 means that there was an error in the correlation measurement.

To calculate the Correlation coefficient, one must first determine the Covariance of the two variables in question. Next, one must calculate each variable's standard deviation. The correlation coefficient is determined by dividing the covariance by the product of the two variables' standard deviations. i.e.,

Where is the correlation coefficient.

Correlation coefficient is 1 shows a perfect positive correlation.

Correlation coefficient of 0.0 shows no relationship between the movement of the two variables.

#2.

POSITIVE CORRELATION:

Positive correlation is a relationship between two variables in which both variables move in tandem—that is, in the same direction. A positive correlation exists when one variable decreases as the other variable decreases, or one variable increases while the other increases.

NEGATIVE CORRELATION:

Negative correlation is a relationship between two variables in which one variable increases as the other decreases, and vice versa. In statistics, a perfect negative correlation is represented by the value -1,

a. Positive correlation

b.Positive correlation

c.Negative correlation.

d. Negative correlation.

#3:

a)

predictor variable (X): Size of an audience

criterion variable (Y): The number of mistakes a student makes during a classroom presentation.

b)

predictor variable (X):  The duration of an overseas tour

criterion variable (Y): The morale among troops overseas

c)

predictor variable (X): Size of a toy in cereal boxes

criterion variable (Y): Preferences for that cereal.