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 \(.22\).

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Definitions:

Drug Tolerance

The body's reduced reaction to a drug over time, which can result in needing higher doses to achieve the same effect.

Symptoms

Physical or mental features that are regarded as indicating a condition of disease, noticeable to a patient, often leading to a diagnosis.

Disinhibitor

A factor or substance that reduces inhibition, potentially leading to decreased self-control or increased impulsivity.

Aggressive Behavior

Actions intended to harm or intimidate others, which can be physical, verbal, or nonverbal in nature.