Let's analyze each statement based on the given relative frequency table to determine which one is false.
We have the following table for Ms. Stewart's students:
[tex]\[
\begin{array}{|c|c|c|c|c|}
\hline & \text{Biology} & \text{Chemistry} & \text{Physical Science} & \text{Total} \\
\hline \text{Freshmen} & 0.15 & 0.1 & 0.2 & 0.45 \\
\hline \text{Sophomores} & 0.2 & 0.25 & 0.1 & 0.55 \\
\hline \text{Total} & 0.35 & 0.35 & 0.3 & 1.0 \\
\hline
\end{array}
\][/tex]
Now, let's check each of the statements:
Statement A: [tex]\(30\% \)[/tex] of her students are in physical science.
From the table, we see that [tex]\[
\text{Total (Physical Science)} = 0.3,
\][/tex]
which corresponds to [tex]\(30\% \)[/tex].
This statement is true.
Statement B: [tex]\(35\% \)[/tex] of her students are in biology.
From the table, we see that [tex]\[
\text{Total (Biology)} = 0.35,
\][/tex]
which corresponds to [tex]\(35\% \)[/tex].
This statement is true.
Statement C: [tex]\(25\% \)[/tex] of her students are in chemistry.
From the table, we see that [tex]\[
\text{Total (Chemistry)} = 0.35,
\][/tex]
which corresponds to [tex]\(35\% \)[/tex], not [tex]\(25\% \)[/tex].
This statement is false.
Statement D: [tex]\(45\% \)[/tex] of her students are freshmen.
From the table, we see that [tex]\[
\text{Total (Freshmen)} = 0.45,
\][/tex]
which corresponds to [tex]\(45\% \)[/tex].
This statement is true.
Therefore, the false statement is:
C. 25% of her students are in chemistry.
