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.

Understand compound interest, continuous compounding, and their implications in financial mathematics.

Apply the properties of logarithms and exponents to simplify expressions.

Perform calculations involving effective yield to evaluate financial investments.

Model exponential growth and decay in various scenarios including population and investment growth.

---

Definitions:

Ventilation

involves the exchange of air between the environment and the lungs, facilitating oxygen and carbon dioxide exchange with the bloodstream.

Terrestrial Vertebrates

Vertebrate animals that live primarily or entirely on land, including mammals, birds, reptiles, and amphibians.

Larynx

The hollow muscular organ forming an air passage to the lungs and holding the vocal cords; it is also known as the voice box.

Pharynx

A muscular tube that connects the mouth and nasal cavity to the esophagus and larynx, playing a key role in swallowing and breathing.