Consider the following data set gathered from 16 year olds where 'violent TV' is the number of hours of aggressive television the teenager reported viewing per week and 'aggression' is their score on an aggression scale where a high score indicates a high level of aggression.
$$\begin{array} { | c | c | }
\hline \text { Violent TV } & \text { Aggression } \
\hline 15 & 53 \
\hline 28 & 52 \
\hline 23 & 56 \
\hline 21 & 65 \
\hline 14 & 27 \
\hline 31 & 83 \
\hline 24 & 65 \
\hline 19 & 58 \
\hline 35 & 83 \
\hline
\end{array}$$
-4) The Pearson correlation result is best reported as:
A) r = .805 with p

Question

Consider the following data set gathered from 16 year olds where 'violent TV' is the number of hours of aggressive television the teenager reported viewing per week and 'aggression' is their score on an aggression scale where a high score indicates a high level of aggression.
 $$\begin{array} { | c | c | } 
\hline \text { Violent TV } & \text { Aggression } \
\hline 15 & 53 \
\hline 28 & 52 \
\hline 23 & 56 \
\hline 21 & 65 \
\hline 14 & 27 \
\hline 31 & 83 \
\hline 24 & 65 \
\hline 19 & 58 \
\hline 35 & 83 \
\hline
\end{array}$$
-4) The Pearson correlation result is best reported as:
A) r = .805 with p < .05
B) r = .805 with p < .01
C) r = .681 with p < .05
D) r = .194 with p < .01

Quizplus · Accepted Answer

To calculate Pearson correlation, we can use a calculator or software. With a calculator, we can use the following formula:
r = (nΣXY - ΣXΣY) / [(nΣX^2 - (ΣX)^2)(nΣY^2 - (ΣY)^2)]^0.5
where n is the sample size, Σ represents the sum, X and Y represent the two variables, and ^0.5 represents the square root.
With the data given above, we can calculate:

n = 9
ΣX = 190
ΣY = 522
ΣX^2 = 5722
ΣY^2 = 35229
ΣXY = 11840

Substituting these values into the above formula, we get:
r = (9(11840) - 190(522)) / [(9(5722) - 190^2)(9(35229) - 522^2)]^0.5
r = 0.805

To determine the p-value, we need to consult a table of critical values of correlation coefficients at a given level of significance and degrees of freedom. With a sample size of 9 and a significance level of 0.01, we have 7 degrees of freedom. Consulting the table, we find that the critical value is 0.725. Since our calculated r value (0.805) is greater than the critical value, we can reject the null hypothesis that the correlation coefficient is zero at the 0.01 level of significance.

Therefore, the best choice is B, which reports the Pearson correlation result as r = 0.805 with p < 0.01.

Consider the Following Data Set Gathered from 16 Year Olds