To determine which statement is false, we will analyze each given statement using the information provided in the relative frequency table.
Relative Frequency Table:
[tex]\[
\begin{tabular}{|c|c|c|c|c|}
\hline & Biology & Chemistry & \begin{tabular}{l}
Physical \\
science
\end{tabular} & Total \\
\hline Freshman & 0.15 & 0.1 & 0.2 & 0.45 \\
\hline Sophomores & 0.2 & 0.25 & 0.1 & 0.55 \\
\hline Total & 0.35 & 0.35 & 0.3 & 1.0 \\
\hline
\end{tabular}
\][/tex]
Now, we will break down and verify each statement:
Statement A: [tex]$30\%$[/tex] of her students are in physical science.
According to the table, the total fraction of students in physical science is given as 0.3, or 30%. Hence, statement A is true.
Statement B: [tex]$45\%$[/tex] of her students are freshmen.
From the table, the total fraction of freshmen is 0.45, or 45%. Therefore, statement B is correct.
Statement C: [tex]$25\%$[/tex] of her students are in chemistry.
Looking at the table, the total fraction of students in chemistry is 0.35, or 35%. Statement C claims that 25% of the students are in chemistry. This statement, therefore, does not align with the data provided in the table. Hence, statement C is false.
Statement D: [tex]$35\%$[/tex] of her students are in biology.
From the table, the total fraction of students in biology is 0.35, or 35%. Therefore, statement D is true.
Conclusion:
Comparing all the statements with the table, it is clear that statement C is the one that is false. It inaccurately states the percentage of students in chemistry.
So, the false statement is:
C. [tex]$25 \%$[/tex] of her students are in chemistry.
