As Part of a Study at a Large University, Data $x _ { 1 } =$

question 8

Short Answer

As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student's grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university): $x _ { 1 } =$ average high school grade in mathematics (HSM)
$x _ { 2 } =$ average high school grade in science (HSS)
$x _ { 3 } =$ average high school grade in English (HSE)
$x _ { 4 } =$ SAT mathematics score (SATM)
$x _ { 5 } =$ SAT verbal score (SATV)

A first-order model was fit to data.

A $95 \%$ confidence interval for $\beta _ { 1 }$ is $( .06 , .22 )$ . Interpret this result.

A) We are $95 \%$ confident that a CS freshman's GPA increases by an amount between .06 and .22 for every 1 -point increase in average H5 math grade, holding $x _ { 2 } - x _ { 5 }$ constant.
B) $95 \%$ of the GPAs fall within .06 to $.22$ of their true values.
C) We are $95 \%$ confident that a CS freshman's HS math grade increases by an amount between .06 and .22 for every 1-point increase in GPA, holding $x _ { 2 } - x _ { 5 }$ constant.
D) We are $95 \%$ confident that the mean GPA of all CS freshmen after three semesters falls between .06 and $.22$ .

• A) We are \(95 \%\) confident that a CS freshman's GPA increases by an amount between .06 and .22 for every 1 -point increase in average H5 math grade, holding \(x _ { 2 } - x _ { 5 }\) constant.
• B) \(95 \%\) of the GPAs fall within .06 to \(.22\) of their true values.
• C) We are \(95 \%\) confident that a CS freshman's HS math grade increases by an amount between .06 and .22 for every 1-point increase in GPA, holding \(x _ { 2 } - x _ { 5 }\) constant.
• D) We are \(95 \%\) confident that the mean GPA of all CS freshmen after three semesters falls between .06 and \(.22\).

---

Definitions:

Willingness to Hurt

An individual's propensity or readiness to cause pain or harm to others, either physically or emotionally.

Minimal Levels

The least or smallest amount or degree of something required, allowed, or possible.

Father Care

The involvement and nurturing behaviors of a father towards his children, contributing to their development and wellbeing.

High Levels of Aggression

Refers to an increased tendency or frequency to engage in behaviors intended to harm or assert dominance over others.