Construct Confidence Intervals for a Mean Response
-In Order for a Company's

Construct Confidence Intervals for a Mean Response
-In order for a company's employees to work at a foreign office, they must take a test in the language of the country where they plan to work. The data below shows the relationship between the number of years that employees have studied a particular language and the grades they received on the proficiency exam. Construct a $95 \%$ confidence interval about the mean value of $\mathrm { y }$ , given $\mathrm { x } = 2.5 , \mathrm { y } = 6.91 \mathrm { x } + 46.26$ , and $\mathrm { s } e = 4.578$ .
$\begin{array}{l|c|c|c|c|c|c|c|c|c|}\text { Number of years, } \mathrm{x} & 3 & 4 & 4 & 5 & 3 & 6 & 2 & 7 & 3 \\\hline \text { Grades on test, } \mathrm{y} & 61 & 68 & 75 & 82 & 73 & 90 & 58 & 93 & 72\end{array}$

A) $( 58.28,68.79 )$
B) $( 51.50,75.57 )$
C) $( 55.12,87.34 )$
D) $( 47.32,72.13 )$