As Part of a Study at a Large University, Data $n = 224$

question 86

Multiple Choice

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) \(95 \%\) of the GPAs fall within .06 to \(.22\) of their true values.
• B) 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.
• C) We are \(95 \%\) confident that the mean GPA of all CS freshmen after three semesters falls between 06 and .22.
• D) 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 HS math grade, holding \(x _ { 2 } - x _ { 5 }\) constant.

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Definitions:

Average Variable Cost

The sum of all costs that fluctuate with production volume, divided by the total amount of goods produced.

Long Run

A period in which all factors of production and costs are variable, allowing for full adjustment to changes.

Variable Factors

Inputs to production that can be adjusted in the short term, such as labor and raw materials.

Fixed Costs

Expenses that do not change with the level of output, such as rent or salaries.