A Collection of Paired Data Consists of the Number of Years

question 42

Multiple Choice

A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test. A computer program was used to obtain the least squares linear regression line and the computer output is shown below. Along with the paired sample data, the program was also given an x value of 2 (years of study) to be used for predicting test score. The regression equation is
$\text { Score }=31.55+10.90 \text { Years. }$
$\begin{array}{lclcc}\text { Predictor } & \text { Coef } & \text { StDev } & \text { T } & \text { P } \\\text { Constant } & 31.55 & 6.360 & 4.96 & 0.000 \\\text { Years } & 10.90 & 1.744 & 6.25 & 0.000\end{array}$
$$\mathrm{S}=5.651 \quad \mathrm{R}-\mathrm{Sq}=83.0 \% \quad \mathrm{R}-\mathrm{Sq}(\text { Adj }) =82.7 \%$$
Predicted values
$\begin{array}{llcc}\text { Fit } & \text { StDev Fit } & 95.0 \% \text { CI } & 95.0 \% \text { PI } \\ 53.35 & 3.168 & (42.72,63.98) & (31.61,75.09) \end{array}$
Use the information in the display to find the value of the linear correlation coefficient r. Determine whether the significant linear correlation between years of study and test scores. Use a significance level of $0.05$ . There are 16 data.

• A) \(r = 0.91\); There is significant linear correlation.
• B) \(\mathrm { r } = 0.83\); There is no significant linear correlation.
• C) \(\mathrm { r } = 0.91\); There is no significant linear correlation
• D) \(r = 0.83\); There is significant linear correlation.

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Definitions:

Adam Smith

An 18th-century Scottish economist and philosopher known as the father of modern economics and author of "The Wealth of Nations."

Opportunity Cost

The cost of forgoing the next best alternative when making a decision, representing the benefits one could have received by taking the alternative action.

Forgone Interest

The potential interest earnings lost by choosing one investment over another or by keeping money in a non-interest-bearing account.

Economic Growth

The increase in the amount of goods and services produced by an economy over time, typically measured as the percent rate of increase in real gross domestic product (GDP).