It Is Debated Whether IQ Scores Influence Criminal Behavior (Either

Essay

It is debated whether IQ scores influence criminal behavior (either directly or indirectly). It is argued that the majority of criminals have an IQ that lies 8 points below (92) the average IQ (100). You draw a random sample of 15 individuals of age 18+, assess the IQ of participants, and ask them about their criminal history (number of offenses committed, not including minor traffic violations). You select an alpha of 0.05. The results of your assessment are to be found in the table presented below.
a. State your null and alternative hypotheses.
b. State your decision rule to determine statistical significance.
c. Utilizing the data from the table presented below:
i. Compute beta (b).
ii. Compute the constant (a).
iii. Determine the strength and direction of the relationship by computing Pearson's r.
iv. Compute r².
v. Compute the prediction error you could possibly have if you know nothing about the distribution of the independent variable (IQ score).
vi. Compute the unexplained variance.
vii. Compute the explained variance.
d. Make a decision.
e. Compute the standard error of estimate.
f. INTERPRET ALL YOUR RESULTS.
$$\begin{array} { | r | r | r | } \hline { \text { Case } } & \text { IQ } ( x ) & \begin{array} { l } \text { No. of } \\\text { offenses } \\( y )\end{array} \\\hline 1 & 90 & 4 \\\hline 2 & 110 & 1 \\\hline 3 & 89 & 4 \\\hline 4 & 95 & 3 \\\hline 5 & 92 & 5 \\\hline 6 & 91 & 4 \\\hline 7 & 102 & 0 \\\hline 8 & 99 & 2 \\\hline 9 & 76 & 3 \\\hline 10 & 99 & 1 \\\hline 11 & 92 & 6 \\\hline 12 & 98 & 1 \\\hline 13 & 111 & 1 \\\hline 14 & 100 & 2 \\\hline 15 & 93 & 6 \\\hline\end{array}$$